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Call number: | 9783319527420:ONLINE Show nearby items on shelf |
Title: | Harmonic Analysis, Partial Differential Equations and Applications In Honor of Richard L. Wheeden |
Author(s): | |
Date: | 2017 |
Size: | 1 online resource (XXIV, 301 p p.) |
ISBN: | 9783319527420 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Harmonic analysis , Partial differential equations , Numerical analysis , Mathematics , Partial Differential Equations , Abstract Harmonic Analysis , Numerical Analysis |
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Call number: | 9781608074891:ONLINE Show nearby items on shelf |
Title: | Microwave mixer technology and applications |
Author(s): |
Bert Henderson Edmar Camargo |
Date: | 2013 |
Publisher: | Artech House |
Size: | 1 online resource (864 p.) |
Contents: | Chapter 1 Origins of Electronic Mixers -- History of Radio Development -- Single Ended Circuits -- Singly Balanced Mixers -- Doubly Balanced Star Circuit -- Special Receiver Architectures -- Harmonic Mixers -- Self-Oscillating Balanced Mixers -- Dis tributed Mixers . Chapter 2 System Parameters and Performance -- System Overview -- Digital Modulation -- Error Performance -- Receiver Architectures -- Mixer Linearity . Noise -- Noise and Distortion in Communication Subsystems -- Dynamic Range . Chapter 3 Semiconductor Modeling -- Modeling Schottky Diodes -- Modeling Bipolar Transistors -- Modeling Field Effect Transistors . Chapter 4 Passive and Active Coupling Structures -- Balun Structure -- Marchand Balun -- Microstrip Baluns -- Lumped Elements -- S lotline Type -- Active Approach -- Hybrid Couplers (Magic-T) -- Quadrature Hybrids -- Appendix 4A Guanella 4-1 Transformer -- Appendix 4B Compensated Balun -- Appendix 4C Active FET Power Divider -- Appendix 4D Alternative FET Power Divider -- Appendix 4E Active FET Combiner |
Chapter 5 Diode Mixer Theory -- History of Linear and Nonlinear Analysis -- Linear Mixer Analysis -- Frequency Conversion Matrix -- Computer Simulation Example -- Large Signal Conversion Analysis -- Subharmonic Mixer -- Balanced Diode Circuits -- Mi xer Circuit Synthesis -- Appendix 5A Parasitic Losses in Diode Mixers -- Appendix 5B Conversion Matrix Including Parasitics -- Appendix 5C Image Imp. and RF-Image Conversion -- Appendix 5D Saleh Exp. Diode Mixer Performance -- Chapter 6 Diode Applications -- Single Ended -- Singly Balanced -- Doubly Balanced -- Triply Balanced -- Quadrature Mixers -- Subharmonic Mixers -- Chapter 7 BJT Mixer Theory -- Low Frequency Mixer -- Conversion Matrix -- Mixer Properties -- Design Study: CDMA Down-Converter -- Ca scode Approach -- Singly Balanced Mixer -- Singly Balanced Subharmonic -- Doubly Balanced Mixer -- WiFi 2.45 GHz Gilbert Mixer -- Differential Triple Level -- Doubly Balanced Subharmonic -- Subharmonic Triple Level -- Appendix 7A Gummel Poon Parameters -- Appendix 7B Spice Parameters . Chapter 8 Bipolar Junction Transistor Applications -- Single Ended -- Parallel Combined Mixers -- Integrated Circuit Topologies -- Doubly Balanced -- Image Reject -- Subharmonic Topologies | |
Chapter 9 CFET Mixer Theory -- Gate LO Injection -- Source LO Injection -- Drain LO Injection -- Resistive Approach -- Cascode Mixer -- Singly Balanced -- Doubly Balanced -- Subharmonic Mixing -- Distributed Mixers -- Appendix 9A NE67300 Parameters -- Chapter 10 Passive FET Applications -- Single Ended -- Floating Approach -- Singly Balanced -- Doubly Balanced -- Distributed GaAs Applications . Chapter 11 Active FET Applications -- Single Ended -- Singly Balanced Doubly Balanced -- Subharmonic Appro ach -- Self-Oscillating FET Mixer -- Distributed Applications | |
ISBN: | 9781608074891 |
Series: | Artech House microwave library |
Series: | eBooks |
Series: | Artech eBooks |
Keywords: | Microwave mixers. |
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Call number: | 9781608071210:ONLINE Show nearby items on shelf |
Title: | Behavioral modeling and linearization of RF power amplifiers |
Author(s): |
John Wood |
Date: | 2014 |
Publisher: | Artech House |
Size: | 1 online resource (362 p.) |
Contents: | Chapter 1 Introduction -- History of Mobile Wireless Communications -- Digital Modulation -- Filters for Digital Communication Systems -- Measures for Digital Communication Signals -- RF Power Amplifiers: Linearity and Efficiency -- Harmonic Loading -- The Doherty Amplifier -- The Polar Amplifier -- High-Efficiency PA Summary -- Linearization Techniques for RF PAs -- Polar Feedback -- Cartesian Feedback -- Feedforward -- Pre-distortion -- Behavioral Modeling -- Chapter 2 Models, Modeling, and Simulation -- Data- or Measurement-Based Models -- Physically Based Models -- Equivalent Circuit Models -- Compact Models -- Behavioral Models -- Function Fitting and Function Approximation -- Model Validation -- Circuit Si mulation -- Electromagnetic Simulation -- Device Physical Simulation -- Thermal Simulation -- System Simulation -- Chapter 3 Linear Systems and Identification -- Linear System Properties -- Instantaneous and Dynamic Systems -- Time Domain or Frequency Dom ain -- Convolution Integral and Impulse Response -- State Space Representation -- Discrete Time Representation -- General Transfer Function Models -- Noise and Disturbance Signals -- General Model Structure -- model Building -- Basis Functions -- Least Sq uares Algorithm -- Error Measures -- System Identification -- Nonlinear System Identification |
Chapter 4 Modeling PA Nonlinearities -- Gain Compression in the PA -- Modeling the CW Input-Output Relationship -- Phase Characteristic - AM-to-PM Behavior -- Two-Tone Analysis -- Comments on the Two-Tone Analysis -- Chapter 5 Memory Effects -- Shor t-Term Memory Effects -- Long-Term Memory Effects -- Matching Networks -- Charge Storage in the Transistor -- Thermal Effects -- Trapping of Charge -- Bias and Supply Lines -- Including Memory Effects in the Nonlinear Model -- Chapter 6 Nonlinear Dynamica l Models -- Volterra Series -- Taylor Series -- Cascade of Linear and Nonlinear Components -- The Higher-Order Kernels -- Discrete-Time Expressions for Volterra Series -- Nonlinear Feedback Model -- Wiener and Hammerstein Models -- Memory Polynomial Model -- Parallel Cascade -- Orthogonal Basis Functions -- Advanced Volterra Series Models -- Dynamic Deviation Model -- Narrowband Approximation- Baseband Volterra Models -- Techniques for Building Volterra Models of Power Amplifiers -- Data Pre-conditioning -- Model Selection -- Model Solution: Parameter Estimation -- Model Validation -- Non-Volterra Models -- Artificial Neural Networks | |
Chapter 7 Digital Pre-Distortion -- Pre-Distortion -- Gain and Bandwidth Concerns -- Pre-Distortion of the Digital Signal -- Digital Pre-Distortion System -- Baseband Signal Processing -- Crest Factor Reduction -- The DPD Function Block -- Adaptive Digital Pre-Distortion -- Indirect Learning DPD System -- Model Reference DPD System -- DPD Coefficient Adaption Techniques -- DPD System Implementation Details -- RF Section -- Data Converters -- Baseband Digital Signal Processing -- Chapter 8 Crest Fact or Reduction of Digital Communication Signals -- Cause of Signal Peaks -- CFR Overview -- Clip-and-Filter Approaches -- Peak Windowing -- Partial Transmit Sequence -- Tone Reservation -- Constellation Extension -- Coding -- CFR for Downlink LTE Using Phas e-Shifted Resource Blocks -- Chapter 9 RF Pre-Distortion -- RFPD vs. DPD -- Implementation -- From RF to Baseband and Back to RF -- Volterra Series Simplification -- RFPD Architecture -- Analyzing and Processing Engine -- Analog Data Path -- Technical Cha llenges and Analog Limitations -- Offsets - Impact on the Pre-distortion Signal -- Peak-to-Average Power Ratio -- Signal Expansion and Compression -- Bandwidth Expansion -- Temperature Effects -- Normalizing the CORR -- Nonlinear Operator Normalization -- SC1894 -- Carrier Aggregation -- Chapter 10 Frequency Domain Models -- Frequency Domain Nonlinear Models . Amplifier 2 Model -- P2D Model -- X-Parameters -- S-Functions Model -- The Cardiff Model | |
ISBN: | 9781608071203 |
Series: | Artech House microwave library. |
Series: | Artech eBooks |
Series: | eBooks |
Keywords: | Amplifiers, Radio frequency. , Amplifiers, Radio frequency. fast |
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Call number: | 9781608070480:ONLINE Show nearby items on shelf |
Title: | Discrete oscillator design |
Author(s): |
Randall W. Rhea |
Date: | 2010 |
Publisher: | Artech House |
Size: | 1 online resource (450 p.) |
Contents: | Chapter 1 Linear Techniques -- Open-Loop Method -- Match Requirements -- Aligning the Maximum Phase Slope -- Stable Amplifier -- Gain Peak at Phase Zero Intersection -- Moderate Gain -- Random Resonator and Amplifier Combination -- Naming Convention s -- Amplifiers for Sustaining Stages -- Bipolar Amplifier Configurations -- Stabilizing Bipolar Amplifiers -- Stabilized FET Amplifier Configurations -- Basic Common Emitter Amplifier -- Statistical Analysis of the Amplifier -- Amplifier with Resistive F eedback -- General-Purpose Resistive-Feedback Amplifier -- Transformer-Feedback Amplifiers -- Monolythic Microwave Integrated Circuit Amplifiers -- Differential Amplifiers -- Phase-Lead Compensation -- Resonators -- R-C Phase Shift Network -- Delay-Line P hase-Shift Network -- L-C Parallel and Series Resonators -- Loaded Q . Unloaded Q -- Resonator Loss -- Colpitts Resonator -- Resonator Coupling -- Matching with the Resonator -- Measuring the Unloaded Q -- Coupled Resonator Oscillator Example -- Resonator Summary -- One-Port Method -- Negative-Resistance Oscillators -- Negative-Conductance Oscillators -- Analyzing Existing Oscillators -- Optimizing the Design |
Chapter 2 Nonlinear Techniques -- Harmonic Balance -- Nonlinear Amplifiers -- Quiescent Current and Compression -- Impedance Shift -- Phase Shift -- Output Spectrum -- Time Domain Waveform -- Conversion Efficiency -- Operating Class -- Nonlinear Ope n-Loop Cascade -- Nonlinear HB Colpitts -- Closing the Loop and Excitation -- Harmonic Balance Colpitts Output Spectrum -- Excitation Current Versus Oscillator Parameters -- Nonlinear Negative-Resistance Oscillator -- Output Coupling -- Coupling Node -- L oad Pulling -- Loaded Q and Load Pulling -- Degree of Coupling -- Loaded Q and Coupling -- Coupling Reactance and Load Pulling -- Coupling Reactance and Harmonics -- Output Coupling Example 2 -- Passive Level Control -- Supply Pushing -- Spurious Modes -- Unstable Amplifiers -- Multiple Phase Zero Crossings -- Parametric Modes -- Multiple Resonance Modes -- Chapter 3 Transient Techniques -- Starting Modes -- Noise Mode of Starting -- Tansient Mode of Starting -- Time Constant of the Supply Step -- Simulat ion Techniques -- SPICE -- Cayenne -- Triggering -- Simulation Techniques for High Loaded Q -- Steady-State Oscillator Waveforms -- Clapp Oscillator Waveforms -- The Resonator Voltage -- Varactor Coupling -- Waveform Derived Output Spectrum | |
Chapter 4 Noise -- Vector Representation of the Oscillator Output -- Jitter -- The Output in the Frequency Domain -- SSB Phase Noise -- Residual FM and Residual PM -- Two-Port Noise -- Acoustic Disturbances -- Predicting Phase Noise -- Linear Time I nvariant Theory -- Extensions to LTI-Based Theory -- Linear Time Variant Theory -- Measuring Phase Noise -- Direct Method with a Spectrum Analyzer -- Selective Receiver Method -- Heterodyne/Counter Method -- Reference Oscillator Method -- Frequency Discri minator Method -- Example Phase-Noise Measurement System -- Designing for Low Phase Noise -- Estimating the Predominant Noise Source -- Reducing Leeson Noise -- Reducing Pushing Induced Noise -- Reducing Buffer Noise -- Reducing Varactor Modulation Noise -- PLL Noise -- Chapter 5 General-Purpose Oscillators -- Oscillators Without Resonators -- R-C Oscillators -- Wien Bridge -- Multivibrators -- Ring Oscillators -- Twin-T Oscillators -- L-C Oscillators -- Colpitts -- Clapp -- Seiler -- Hartley -- Pierce -- Coupled Series Resonator -- Rhea -- Coupled Parallel Resonator -- Gumm -- Oscillator Topology Selection | |
Chapter 6 Distributed Oscillators -- Resonator Technologies -- Lumped and Distributed Equivalents -- Quarter-Wavelength Resonators -- Ceramic-Loaded Coaxial Resonators -- Capacitor-Loaded Quarter-Wavelength Resonator -- Distributed Oscillator Exampl es -- Negative-Resistance Hybrid Oscillator -- Negative-Resistance High-Power 1 GHz Oscillator -- Quarter-Wavelength Hybrid Oscillator -- Simple Hybrid Coaxial Resonator MMIC -- Probe-Coupled Coaxial Resonator Bipolar -- End-Coupled Hybrid Half-Wavelength Bipolar -- Helical Transmission Line Resonator Bipolar -- DRO Oscillators -- Dielectric Resonator Basic Properties -- Dielectric Resonator Resonant Frequency -- Dielectric Resonator Unloaded Q -- Dielectric Resonator Coupling -- Chapter 7 Tuned Oscillato rs -- Resonator Tuning Bandwidth -- Resonator Voltage -- Permeability Tuning -- Tunable Oscillator Examples -- Permeability Tuned Colpitts JFET -- Vackar JFET VCO -- Hybrid Negative Resistance VCO -- Capacitor-Transformed Negative-Resistance VCO -- Negati ve-Resistance VCO with Transformer -- Negative-Conductance VCO -- Hybrid Coaxial Resonator MMIC -- Loaded Quarter-Wavelength MMIC -- Seiler Coaxial-Resonator CC VCO -- YIG Oscillators | |
Chapter 8 Piezoelectric Oscillators -- Bulk Quartz Resonators -- Quartz Blank Cuts -- Crystal Resonator Model -- Calculating Crystal Resonator Parameters -- Crystal Resonator Frequency Pulling -- Inverted-Mesa Crystal Resonators -- Crystal Oscillato r Operating Mode -- Crystal Oscillator Frequency Accuracy -- Temperature Effects on Crystal Oscillators -- Crystal Resonator Drive Level -- Crystal Resonator Spurious Modes -- Crystal Resonator Aging -- Crystal Resonator Noise -- Crystal Resonator Acceler ation Effects -- Crystal Resonator Standard Holders -- Fundamental Mode Crystal Oscillators -- Miller JFET Crystal -- Colpitts Bipolar Crystal -- Colpitts JFET Crystal -- Pierce Bipolar Crystal -- Pierce MMIC Crystal -- Pierce Inverter TTL Crystal -- Pier ce Inverter CMOS Crystal -- Butler Dual Bipolar Crystal -- Driscoll Bipolar Crystal -- Inverted-Mesa Pierce Bipolar Crystal -- Overtone Mode Crystal Oscillators -- Colpitts Overtone Bipolar Crystal -- CB Butler Overtone Bipolar Crystal -- CC Butler Overt one Bipolar Crystal -- Oscillator with Frequency Multiplier -- Crystal Oscillator Starting -- Surface Acoustic Wave Resonators -- SAW Resonator Models -- SAW Resonator Frequency Stability -- SAW Oscillators -- SAW 1-Port Colpitts Bipolar -- SAW 1-Port But ler Bipolar -- SAW 2-Port Pierce MMIC -- Piezoelectric Ceramic Resonators -- Ceramic Resonator Models -- Ceramic Resonator Accuracy and Stability -- Ceramic Resonator Oscillators -- MEMS and FBAR Resonators | |
ISBN: | 9781608070473 |
Series: | Artech house microwave library |
Series: | eBooks |
Series: | Artech eBooks |
Keywords: | Harmonic oscillators, Design. , Oscillators, Electric, Design. |
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Call number: | 0471975486:ONLINE Show nearby items on shelf |
Title: | Power System Harmonic Analysis |
Author(s): |
Arrillaga |
Date: | 1997 |
Publisher: | Wiley |
Size: | 1 online resource (383 p.) |
ISBN: | 9780471975489 |
Series: | eBooks |
Series: | Wiley Online Library |
Series: | Wiley 2016 package purchase |
Keywords: | Electrical & Electronics Engineering |
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Call number: | TA355.I519::2014 Show nearby items on shelf |
Title: | Engineering vibration |
Author(s): |
DANIEL J. INMAN |
Date: | 2014 |
Edition: | Fourth edition. |
Publisher: | Boston : Pearson |
Size: | 707 p |
Contents: | 1. Introduction to vibration and the free response -- 2. Response to harmonic excitation -- 3. General forced response -- 4. Multiple-degree-of-freedom systems -- 5. Design for vibration suppression -- 6. Distributed-parameter systems -- 7. Vibratio n testing and experimental modal analysis -- 8. Finite element method -- Appendices. |
ISBN: | 9780132871693 |
Keywords: | Vibration |
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Call number: | SPRINGER-2016-9783319397801:ONLINE Show nearby items on shelf |
Title: | Extensions of Positive Definite Functions Applications and Their Harmonic Analysis |
Author(s): |
Palle Jorgensen |
Date: | 2016 |
Size: | 1 online resource (9 p.) |
Note: | 10.1007/978-3-319-39780-1 |
ISBN: | 9783319397801 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 2160 |
Keywords: | Mathematics , Topological groups , Lie groups , Harmonic analysis , Fourier analysis , Functional analysis , Probabilities , Mathematical physics , Mathematics , Abstract Harmonic Analysis , Topological Groups, Lie Groups , Fourier Analysis , Functional Analysis , Mathematical Physics , Probability Theory and Stochastic Processes |
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Call number: | SPRINGER-2016-9783319300344:ONLINE Show nearby items on shelf |
Title: | An Introductory Course in Lebesgue Spaces |
Author(s): |
Rene Erlin Castillo |
Date: | 2016 |
Size: | 1 online resource (461 p.) |
Note: | 10.1007/978-3-319-30034-4 |
Contents: | Convex Functions and Inequalities -- Lebesgue Sequence Spaces -- Lebesgue Spaces -- Distribution Function and Non-Increasing Rearrangement -- Weak Lebesgue Spaces -- Lorentz Spaces -- Non-Standard Lebesgue Spaces -- Interpolation of Operators -- Ma ximal Operator -- Integral Operators -- Convolution and Potentials -- Appendices |
ISBN: | 9783319300344 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Mathematics , Abstract Harmonic Analysis , Functional Analysis |
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Call number: | SPRINGER-2016-9783319299921:ONLINE Show nearby items on shelf |
Title: | Spectral Theory and Mathematical Physics |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (3 p.) |
Note: | 10.1007/978-3-319-29992-1 |
Contents: | Preface -- Lower bounds for sojourn time in a simple shape resonance model -- Spectral properties for Hamiltonians of weak interactions -- Magnetic Laplacian in sharp three-dimensional cones -- Spectral clusters for magnetic exterior problems -- Th e spectral shift function and the Witten index -- Stahl’s theorem (aka BMV conjecture): insights and intuition on its proof -- Some estimates regarding integrated density of states for random Schrödinger operator with decaying random potentials -- Boun dary values of resolvents of self-adjoint operators in Krein spaces and applications to the Klein-Gordon equation -- Levinson’s theorem: an index theorem in scattering theory -- Counting function of magnetic resonances for non-definite sign perturbation s -- Harmonic analysis and random Schrödinger operators |
ISBN: | 9783319299921 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Operator Theory: Advances and Applications: 254 |
Keywords: | Mathematics , Functional analysis , Operator theory , Partial differential equations , Mathematical physics , Mathematics , Functional Analysis , Operator Theory , Mathematical Physics , Partial Differential Equations |
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Call number: | SPRINGER-2016-9783319295589:ONLINE Show nearby items on shelf |
Title: | Quantization on Nilpotent Lie Groups |
Author(s): |
Veronique Fischer |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (557 p.) |
Note: | 10.1007/978-3-319-29558-9 |
Contents: | Preface -- Introduction -- Notation and conventions -- 1 Preliminaries on Lie groups -- 2 Quantization on compact Lie groups -- 3 Homogeneous Lie groups -- 4 Rockland operators and Sobolev spaces -- 5 Quantization on graded Lie groups -- 6 Pseudo-d ifferential operators on the Heisenberg group -- A Miscellaneous -- B Group C* and von Neumann algebras -- Schrödinger representations and Weyl quantization -- Explicit symbolic calculus on the Heisenberg group -- List of quantizations -- Bibliography -- Index |
ISBN: | 9783319295589 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Mathematics: 314 |
Keywords: | Mathematics , Topological groups , Lie groups , Harmonic analysis , Functional analysis , Mathematical physics , Mathematics , Topological Groups, Lie Groups , Abstract Harmonic Analysis , Functional Analysis , Mathematical Physics |
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Call number: | SPRINGER-2016-9783319278735:ONLINE Show nearby items on shelf |
Title: | New Trends in Applied Harmonic Analysis Sparse Representations, Compressed Sensing, and Multifractal Analysis |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (19 p.) |
Note: | 10.1007/978-3-319-27873-5 |
Contents: | Multifractal Analysis of Cantor-like Measures -- Multifractal Analysis and Wavelets -- An Introduction to Mandelbrot Cascades -- Lebesgue-type Inequalities for Greedy Approximation -- Results on Non-linear Approximation for Wavelet Bases in Weighte d Function Spaces -- Consequences of the Marcus/Spielman/Srivastava Solution of the Kadison-Singer Problem -- Model Sets and New Versions pf Shannon Sampling Theorem -- Stylometry and Mathematical Study of Authorship -- Thoughts on Numerical and Conceptua l Harmonic Analysis |
ISBN: | 9783319278735 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Measure theory , Computer science , Computer mathematics , Mathematics , Fourier Analysis , Abstract Harmonic Analysis , Signal, Image and Speech Processing , Measure and Integration , Mathematical Applications in Computer Science |
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Call number: | SPRINGER-2016-9783319276984:ONLINE Show nearby items on shelf |
Title: | Moving Interfaces and Quasilinear Parabolic Evolution Equations |
Author(s): |
Jan Prüss |
Date: | 2016 |
Size: | 1 online resource (609 p.) |
Note: | 10.1007/978-3-319-27698-4 |
Contents: | Preface -- Basic Notations -- General References -- Part I Background -- 1Problems and Strategies -- 2.Tools from Differential Geometry -- Part II Abstract Theory -- 3Operator Theory and Semigroups -- 4.Vector-Valued Harmonic Analysis -- 5.Quasilin ear Parabolic Evolution Equations -- Part III Linear Theory -- 6.Elliptic and Parabolic Problems -- 7.Generalized Stokes Problems -- 8.Two-Phase Stokes Problems -- Part IV Nonlinear Problems -- 9.Local Well-Posedness and Regularity -- 10.Linear Stability of Equilibria -- 11.Qualitative Behaviour of the Semiows -- 12.Further Parabolic Evolution Problems -- Biographical Comments -- Outlook and Future Challenges -- References -- List of Figures -- List of Symbols -- Subject Index |
ISBN: | 9783319276984 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Monographs in Mathematics: 105 |
Keywords: | Mathematics , Functional analysis , Partial differential equations , Physics , Mathematics , Partial Differential Equations , Mathematical Methods in Physics , Functional Analysis |
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Call number: | SPRINGER-2016-9783319276663:ONLINE Show nearby items on shelf |
Title: | The Spectrum of Hyperbolic Surfaces |
Author(s): |
Nicolas Bergeron |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (370 p.) |
Note: | 10.1007/978-3-319-27666-3 |
Contents: | Preface -- Introduction -- Arithmetic Hyperbolic Surfaces -- Spectral Decomposition -- Maass Forms -- The Trace Formula -- Multiplicity of lambda1 and the Selberg Conjecture -- L-Functions and the Selberg Conjecture -- Jacquet-Langlands Corresponde nce -- Arithmetic Quantum Unique Ergodicity -- Appendices -- References -- Index of notation -- Index -- Index of names |
ISBN: | 9783319276663 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Dynamics , Ergodic theory , Hyperbolic geometry , Mathematics , Hyperbolic Geometry , Abstract Harmonic Analysis , Dynamical Systems and Ergodic Theory |
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Call number: | SPRINGER-2016-9783319274669:ONLINE Show nearby items on shelf |
Title: | Methods of Fourier Analysis and Approximation Theory |
Author(s): | |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (258 p.) |
Note: | 10.1007/978-3-319-27466-9 |
Contents: | 1. Introduction -- 2. Fourier analysis -- 2.1. Parseval frames -- 2.2. Hyperbolic Hardy classes and logarithmic Bloch spaces -- 2.3. Logan's and Bohman's extremal problems -- 2.4. Weighted estimates for the Hilbert transform -- 2.5. Q-Measures and uniqueness sets for Haar series -- 2.6. O-diagonal estimates for Calderón-Zygmund operators -- 3. Function spaces of radial functions -- 3.1. Potential spaces of radial functions -- 3.2. On Leray's formula -- 4. Approximation theory -- 4.1. Approximation order of Besov classes -- 4.2. Ulyanov inequalities for moduli of smoothness -- 4.3. Approximation order of Besov classes -- 5. Optimization theory and related topics -- 5.1. The Laplace-Borel transform -- 5.2. Optimization control problems -- 2 Michael Ruzhansky and Sergey Tikhonov.-5.3. Optimization control problems for parabolic equation -- 5.4. Numerical modeling of the linear filtration -- References. |
ISBN: | 9783319274669 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Numerical analysis , Mathematics , Fourier Analysis , Abstract Harmonic Analysis , Numerical Analysis |
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Call number: | SPRINGER-2016-9783319256139:ONLINE Show nearby items on shelf |
Title: | An Introduction to Frames and Riesz Bases |
Author(s): |
Ole Christensen |
Date: | 2016 |
Edition: | 2nd ed. 2016 |
Size: | 1 online resource (5 p.) |
Note: | 10.1007/978-3-319-25613-9 |
Contents: | Frames in Finite-dimensional Inner Product Spaces -- Infinite-dimensional Vector Spaces and Sequences -- Bases -- Bases and their Limitations -- Frames in Hilbert Spaces -- Tight Frames and Dual Frame Pairs -- Frames versus Riesz Bases -- Selected Topics in Frame Theory -- Frames of Translates -- Shift-Invariant Systems in l2(R) -- Gabor Frames in L2(R) -- Gabor Frames and Duality -- Selected Topics on Gabor Frames -- Gabor Frames in ℓ2(Z),L2(0,L),CL -- General Wavelet Frames in L2(R) -- Dyadic W avelet Frames for L2(R) -- Frame Multiresolution Analysis -- Wavelet Frames via Extension Principles -- Selected Topics on Wavelet Frames -- Generalized Shift-Invariant Systems in L2(Rd) -- Frames on Locally Compact Abelian Groups -- Perturbation of Frame s -- Approximation of the Inverse Frame Operator -- Expansions in Banach Spaces. Appendix |
ISBN: | 9783319256139 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Operator theory , Mathematics , Functional Analysis , Abstract Harmonic Analysis , Operator Theory , Signal, Image and Speech Processing |
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Call number: | SPRINGER-2016-9783319187969:ONLINE Show nearby items on shelf |
Title: | Nigel J. Kalton Selecta Volume 1 |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (771 p.) |
Note: | 10.1007/978-3-319-18796-9 |
Contents: | Preface -- 1.Nigel Kalton's CV -- 2.Nonlocally Convex Spaces and Sub measures -- 3.Differential Games -- 4.Operator Theory -- 5.Harmonic Analysis and PDEs |
ISBN: | 9783319187969 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Functional analysis , Applied mathematics , Engineering mathematics , History , Mathematics , Functional Analysis , History of Mathematical Sciences , Applications of Mathematics |
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Call number: | SPRINGER-2016-9781493934089:ONLINE Show nearby items on shelf |
Title: | Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, Positive Definite Matrix Space and Generalizations |
Author(s): |
Audrey Terras |
Date: | 2016 |
Edition: | 2nd ed. 2016 |
Size: | 1 online resource (21 p.) |
Note: | 10.1007/978-1-4939-3408-9 |
ISBN: | 9781493934089 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Applied mathematics , Engineering mathematics , Geometry , Number theory , Combinatorics , Statistics , Mathematics , Abstract Harmonic Analysis , Number Theory , Geometry , Combinatorics , Applications of Mathematics , Statistical Theory and Methods |
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Call number: | SPRINGER-2014-9789400773417:ONLINE Show nearby items on shelf |
Title: | Laser - Surface Interactions [electronic resource] |
Author(s): |
Rashid A Ganeev |
Date: | 2014 |
Publisher: | Dordrecht : Springer Netherlands : Imprint: Springer |
Size: | 1 online resource |
Note: | This book is about the interaction of laser radiation with various surfaces at variable parameters of radiation. As a basic principle of classification we chose the energetic or intensity level of interaction of laser radiationwith the surfaces. Thes e two characteristics of laser radiation are the most important parameters defining entire spectrum of the processes occurring on the surfaces during interaction with electromagnetic waves. This is a first bookcontaining a whole spectrum of the laser-surf ace interactions distinguished by the ranges of used laser intensity. It combines the surface response starting from extremely weak laser intensities (~1 W cm-2) up to the relativisticintensities (~1020 W cm-2 and higher). The book provides the basic info rmation about lasers and acquaints the reader with both common applications of laser-surface interactions (laser-related printers, scanners, barcode readers, discs,material processing, military, holography, medicine, etc) and unusual uses of the processes on the surfaces under the action of lasers (art conservation, rangefinders and velocimeters, space and earth explorations, surface engineeringand ablation, and others). The scientific applications of laser-surfaces interactions (surface optical nonlinear ities, surface enhanced Raman spectroscopy, surface nanostructuring, nanoripples and clusters formation, X-ray lasers andharmonic generation from the surfaces) are discussed from the point of view of the close relations between the properties of surface a nd matter, which is a cornerstone of most of studies of materials. The novelty of the approachdeveloped in Laser - Surface Interactions is related with the interconnection of scientific studies with numerous applications of the laser-surface interactions separated in different chapters by the ranges of laser intensities. Wepresent most recent achievements in this field. The book provides valuable information for different ranges of reader's preparedness |
Contents: | 1 Principles of Lasers and Laser |
Surface Interactions | |
2 Interaction of Low | |
Power Laser Radiation with Surfaces | |
3 Analysis of Surface Optical Nonlinearities | |
4 Laser Cleaning of Art. 5 Nanoripples Formation on the Surfaces | |
6 Surface Engineering and Ablation | |
7 Ablation of Clusters from Surfaces for Harmonic Generation of Laser Radiation | |
8 X | |
ray Lasers, Plasma Properties, and Harmonic Generation From Surfaces | |
ISBN: | 9789400773417 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Surfaces (Physics) |
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Call number: | SPRINGER-2014-9783662436967:ONLINE Show nearby items on shelf |
Title: | Semigroups, Boundary Value Problems and Markov Processes [electronic resource] |
Author(s): |
Kazuaki Taira |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and ellipticboundary value probl ems. The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of ellipticboundary value problems provides a general clas s of Feller semigroups in functional analysis. As an application, the author constructs a general class of Markov processes in probability in which a Markovian particle moves both by jumpsand continuously in the state space until it 'dies' at the time whe n it reaches the set where the particle is definitely absorbed. Augmenting the 1st edition published in 2004, this edition includes four new chapters and eightre-worked and expanded chapters. It is amply illustrated and all chapters are rounded off with N otes and Comments where bibliographical references are primarily discussed. Thanks to the kind feedback from many readers, some errors inthe first edition have been corrected. In order to keep the book up-to-date, new references have been added to the bib liography. Researchers and graduate students interested in PDEs, functional analysis and probability will find thisvolume useful |
Contents: | 1.Introduction and Main Results |
Part I Elements of Analysis | |
2.Elements of Probability Theory | |
3.Elements of Functional Analysis | |
4.Theory of Semigroups | |
Part II Elements of Partial Differential Equations | |
5.Theory of Distributions | |
6.Sobolev and Besov Spaces | |
7.Theory of Pseudo | |
Differential Operators | |
8.Waldenfels Operators and Maximum Principles | |
Part III Markov Processes, Semigroups and Boundary Value problems | |
9.Markov Processes, Transition Functions and Feller Semigroups | |
10.Feller Semigroups and Elliptic Boundary Value Problems | |
11.Proof of Theorem 1.3 | |
12.Ma | |
ISBN: | 9783662436967 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Differential equations, partial , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783642344442:ONLINE Show nearby items on shelf |
Title: | Neuromathematics of Vision [electronic resource] |
Author(s): |
Giovanna Citti Alessandro Sarti |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | This book is devoted to the study of the functional architecture of the visual cortex. Its geometrical structure is the differential geometry of the connectivity between neural cells. This connectivity is building and shapingthe hidden brain structur es underlying visual perception. The story of the problem runs over the last 30 years, since the discovery of Hubel and Wiesel of the modular structure of the primary visual cortex, and slowly cams towards atheoretical understanding of the experimental da ta on what we now know as functional architecture of the primary visual cortex. Experimental data comes from several domains: neurophysiology, phenomenology of perception andneurocognitive imaging. Imaging techniques like functional MRI and diffusion tens or MRI allow to deepen the study of cortical structures. Due to this variety of experimental data, neuromathematematics deals with modelling bothcortical structures and perceptual spaces. From the mathematical point of view, neuromathematical call for new instruments of pure mathematics: sub-Riemannian geometry models horizontal connectivity, harmonic analysis in noncommutative groups allows to understand pinwheels structure, as well as non-linear dimensionality reduction is at the base of many neural mor phologies and possibly of the emergence of perceptual units. But at the center of theneurogeometry is the problem of harmonizing contemporary mathematical instruments with neurophysiological findings and phenomenological experiments in an unitary science of vision. The contributions to this book come from the veryfounders of the discipline |
Contents: | Landmarks for Neurogeometry |
Shape, Shading, Brain and Awareness | |
From functional architectures to percepts: a neuro mathematical Approach | |
Cuspless Sub | |
Riemannian Geodesics within the Euclidean Motion Group SE(d) | |
Psychophysics, Gestalts and Games | |
Remarks on invariance in the primary visual systems of mammals | |
Hebbian Learning of the Statistical and Geometrical Structure of Visual Input | |
ISBN: | 9783642344442 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Lecture Notes in Morphogenesis, 2195-1934 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer vision , Biomedical engineering , Consciousness |
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Call number: | SPRINGER-2014-9783319078427:ONLINE Show nearby items on shelf |
Title: | Probability on Compact Lie Groups [electronic resource] |
Author(s): |
David Applebaum |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Probability theory on compact Lie groups deals with the interaction between chance and symmetry, a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applicationsin statistics and engineering (par ticularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topicspresented are: the study of measures via the non-commutative F ourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures, and the statistical problem of deconvolution. Theemphasis on compact (rather than general) Lie groups helps readers to get acquaint ed with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance ofthese groups for applications. The book is primarily aimed at researchers working in probability, stochast ic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists,statisticians and engineers who are working on related applications. A background in first year graduate level measure theoreti c probability and functional analysis is essential a background in Lie groups and representation theory iscertainly helpful but the first two chapters also offer orientation in these subjects |
Contents: | Introduction |
1.Lie Groups | |
2.Representations, Peter | |
Weyl Theory and Weights | |
3.Analysis on Compact Lie Groups | |
4.Probability Measures on Compact Lie Groups | |
5.Convolution Semigroups of Measures | |
6.Deconvolution Density Estimation | |
Appendices | |
Index | |
Bibliography | |
ISBN: | 9783319078427 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Probability Theory and Stochastic Modelling, 2199-3130 : v70 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Harmonic analysis , Fourier analysis , Functional analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319062662:ONLINE Show nearby items on shelf |
Title: | Operator Theory in Harmonic and Non-commutative Analysis [electronic resource] : 23rd International Workshop in Operator Theory and its Applications, Sydney, July 2012 |
Author(s): |
Joseph A Ball Michael A Dritschel A.F.M Elst Pierre Portal Denis Potapov |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This book comprisesthe proceedings of the XXIII International Workshop on Operator Theory and its Applications (IWOTA 2012), which was held at the University of New South Wales (Sydney, Australia) from 16 July to 20 July 2012.It includes twelve artic les presenting both surveys of current research in operator theory and original results. The contributors are A. Amenta P. Auscher and S. Stahlhut W. Bauer C. Herrera Yaez and N. Vasilevski C.C. Cowen, S. Jungand E. Ko R.E. Curto, I.S. Hwang and W.Y. Lee S. Dey and K.J. Haria F. Gesztesy and R. Weikard G. Godefroy B. Jefferies S. Patnaik and G. Weiss W.J. Ricker A. Skripka |
Contents: | Introduction |
Tent Spaces over Metric Measure Spaces under Doubling and Related Assumptions | |
Remarks on Functional Calculus for Perturbed First | |
order Dirac Operators | |
(m, ) | |
Berezin Transform and Approximation of Operators on Weighted Bergman Spaces over the Unit Ball | |
Normal and Cohyponormal Weighted Composition Operators on H2 | |
A Subnormal Toeplitz Completion Problem | |
Generalized Repeated Interaction Model and Transfer Functions | |
Some Remarks on the Spectral Problem Underlying the CamassaHolm Hierarchy | |
Remarks on Spaces of Compact Operators between Reflexive Banach Space | |
ISBN: | 9783319062662 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Operator Theory: Advances and Applications, 0255-0156 : v240 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Operator theory |
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Call number: | SPRINGER-2014-9783319057927:ONLINE Show nearby items on shelf |
Title: | Principles of Harmonic Analysis [electronic resource] |
Author(s): |
Anton Deitmar Siegfried Echterhoff |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respectivegeneralizations to non-abelian grou ps, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelicgroups, as well as a complementary section on direct an d projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonicanalysis and for researchers seeking to apply it |
Contents: | 1. Haar Integration |
2. Banach Algebras | |
3. Duality for Abelian Groups | |
4. The Structure of LCA | |
Groups | |
5. Operators on Hilbert Spaces | |
6. Representations | |
7. Compact Groups | |
8. Direct Integrals | |
9. The Selberg Trace Formula | |
10. The Heisenberg Group | |
11. SL2(R) | |
12. Wavelets | |
13. p | |
adic numbers and adeles | |
A. Topology | |
B. Measure and Integration | |
C: Functional Analysis | |
ISBN: | 9783319057927 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Visualization |
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Call number: | SPRINGER-2014-9783319025506:ONLINE Show nearby items on shelf |
Title: | Fourier Analysis [electronic resource] : Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations |
Author(s): |
Michael Ruzhansky Ville Turunen |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, andtime-frequency analysis. This coll ection of 20 refereed articles is based on selected talksgiven at the international conference Fourier Analysis and Pseudo-Differential Operators, June 2530, 2012, at Aalto University,Finland, and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012 it was also the 6th meeting in the series FourierAnalysis and Partial Differential Equations. |
Contents: | Preface |
Contributions by N. Bez, M. Sugimoto, Tang Bao Ngoc Bui, M. Reissig, F. Colombini, D. Del Santo, F. Fanelli, G. Metivier, E. Cordero, F. Nicola, L. Rodino, S. Coriasco, K. Johansson, J. Toft, V. Fischer, M. Ruzhansky, G.Garello, A. Morando, D. Grieser, E. Hunsicker, N. Habal, W. Rungrottheera, B | |
W. Schulze, C. Iwasaki, B. Kanguzhin, N. Tokmagambetov, S. Katayama, H. Kubo, M. Lassas, T. Zhou, T. Matsuyama, T. Nishitani, S. Serovajsky, K. Shakenov, S. Tikhonov, M. Zeltser, Y. Wakasugi, K. Yagdjian. | |
ISBN: | 9783319025506 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Global analysis , Operator theory , Differential equations, partial , Sequences (Mathematics) |
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Call number: | SPRINGER-2014-9783319018065:ONLINE Show nearby items on shelf |
Title: | Harmonic and Complex Analysis and its Applications [electronic resource] |
Author(s): |
Alexander Vasil'ev |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This volume highlights the main results of the research performed within the network Harmonic and Complex Analysis and its Applications (HCAA), which was a five-year (20072012) European Science Foundation Programmeintended to explore and to strengthe n the bridge between two scientific communities: analysts with broad backgrounds in complex and harmonic analysis and mathematical physics, and specialists in physics and applied sciences. Itcoordinated actions for advancing harmonic and complex analysis and for expanding its application to challenging scientific problems. Particular topics considered by this Programme included conformal and quasiconformal mappings,potential theory, Banach spaces of analytic functions and their applications to the problem s of fluid mechanics, conformal field theory, Hamiltonian and Lagrangian mechanics, and signal processing. This book is a collection of surveyswritten as a result of activities of the Programme and will be interesting and useful for professionals and novi ces in analysis and mathematical physics, as well as for graduate students. Browsing the volume, the reader willundoubtedly notice that, as the scope of the Programme is rather broad, there are many interrelations between the various contributions, which can be regarded as different facets of a common theme |
Contents: | L.D. Abreu, H.G. Feichtinger: Function spaces of polyanalytic functions |
F. Bracci, M.D. Contreras, S. Daz | |
Madrigal,A. Vasil'ev: Classical and stochastic Lwner | |
Kufarev equations | |
M. Elin, F. Jacobzon, M. Levenshtein, D. Shoikhet: The Schwarz Lemma. Rigidity and Dynamics | |
H.G. Feichtinger, M. Pap: Coorbit theory and Bergman spaces | |
S.J. Gardiner, T. Sjdin: Quadrature domains and their two | |
phase counterparts | |
B. Gustafsson: Exponential transforms, resultants and moments | |
M. Schlichenmaier: From the Virasoro Algebra to KricheverNovikov Type Algebras and Beyond | |
ISBN: | 9783319018065 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Functional analysis , Functions of complex variables , Potential theory (Mathematics) |
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Call number: | SPRINGER-2014-9783034808408:ONLINE Show nearby items on shelf |
Title: | Variable Lebesgue Spaces and Hyperbolic Systems [electronic resource] |
Author(s): |
David Cruz-Uribe Alberto Fiorenza Michael Ruzhansky Jens Wirth Sergey Tikhonov |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesguespaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integralswith non-standard growth conditions. They ha ve applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function spaceproperties of variable Lebesgue spaces proofs are modeled on the classic al theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such asconvolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted. Part 2 gives an overview of the asymptotic properties of solutions to hyperbolicequations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems withtime-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Ca uchy problems are constructed as oscillatory integrals by working in appropriatetime-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lo wer order terms can change asymptotic properties and thuscomplements the exposition |
Contents: | Part I: Introduction to the Variable Lebesgue Spaces |
Introduction and motivation | |
Properties of variable Lebesgue spaces | |
The Hardy | |
Littlewood maximal operator | |
Extrapolation in variable Lebesgue spaces | |
Part II:Asymptotic Behaviour of Solutions to Hyperbolic Equations and Systems | |
Equations with constant coefficients | |
Some interesting model cases | |
Time | |
dependent hyperbolic systems | |
Effective lower order perturbations | |
Examples and counter | |
examples | |
Related topics | |
ISBN: | 9783034808408 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Advanced Courses in Mathematics - CRM Barcelona, 2297-0304 : v27 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral equations , Differential equations, partial , Functions, special |
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Call number: | SPRINGER-2014-9783034806947:ONLINE Show nearby items on shelf |
Title: | A Course on Integration Theory [electronic resource] : including more than 150 exercises with detailed answers |
Author(s): |
Nicolas Lerner |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathodory Theorem. It also includes some elementary properties ofHausdorff measures as we ll as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change-of-variables formulas as well as the constructionand study of classical Cantor sets are treate d in detail. Classical convolution inequalities, such as Young's inequality and Hardy-Littlewood-Sobolev inequality, are proven. Further topics include the Radon-Nikodym theorem, notions ofharmonic analysis, classical inequalities and interpolation theore ms including Marcinkiewicz's theorem, and the definition of Lebesgue points and the Lebesgue differentiation theorem. Each chapter ends with a large number of exercisesand detailed solutions. A comprehensive appendix provides the reader with various eleme nts of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. It also provides more advancedmaterial such as some basic properties of cardinals and ordinals which are useful for the study of measurabi lity |
Contents: | 1 Introduction |
2 General theory of integration | |
3 Construction of the Lebesgue measure on R^d | |
4 Spaces of integrable functions | |
5 Integration on a product space | |
6 Diffeomorphisms of open subsets of R^d and integration | |
7 Convolution | |
8 Complex measures | |
9 Harmonic analysis | |
10 Classical inequalities | |
ISBN: | 9783034806947 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2014-9783034806480:ONLINE Show nearby items on shelf |
Title: | Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation [electronic resource] : 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011 |
Author(s): |
Manuel Cepedello Boiso Hkan Hedenmalm Marinus A Kaashoek Alfonso Montes Rodrguez Sergei Treil |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This book contains a collection of research articles and surveys on recent developments on operator theory as well as its applications covered in the IWOTA 2011 conference held at Sevilla University in the summer of 2011. Thetopics includespectral th eory, differential operators, integral operators, composition operators, Toeplitz operators, andmore.The book also presents a largenumber of techniques in operator theory |
Contents: | Israel Gohberg Memorial Session |
Research work of Israel Gohberg | |
Some new refined Hardy type inequalities with breaking points p=2 or p=3 | |
Non | |
negative self | |
adjoint extensions in rigged Hilbert space | |
Matrices with bidiagonal decomposition, accurate computations and corner cutting algorithms | |
Boundary | |
value problems for higher | |
order elliptic equations in non | |
smooth domains | |
Additive maps preserving the inner local spectral radius | |
and more | |
ISBN: | 9783034806480 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Operator Theory: Advances and Applications, 0255-0156 : v236 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Operator theory , Differential Equations , Systems theory |
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Call number: | SPRINGER-2014-9783034806220:ONLINE Show nearby items on shelf |
Title: | Real Quaternionic Calculus Handbook [electronic resource] |
Author(s): |
Joo Pedro Morais Svetlin Georgiev Wolfgang Sprig |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Real quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativity, electrodynamics, spin etc., it has developed into a body of material that interacts with many branches of mathematics, suchas complex analysis, harmonic analysis, differential geometry, and differential equations. It is also a ubiquitous factor in the description and elucidation of problems in mathematical physics. In the meantime real quaternion analysishas become a well established branch in ma thematics and has been greatly successful in many different directions. This book is based onconcrete examples and exercises rather than general theorems, thus making it suitable for anintroductory one- or two-semester undergraduate course on some of the major aspects of real quaternion analysis in exercises. Alternatively, it may be used for beginning graduate level courses and as a reference work. With exercises atthe end of each chapter and its straightforward writing style the book addresses readers w ho have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as real and complex analysis,ordinary differential equations, partial differential equations, and theory of distributions |
Contents: | 1 An introduction to quaternions |
2 Quaternions and spatial rotation | |
3 Quaternion sequences | |
4 Quaternion series and infinite products | |
5 Exponents and logarithms | |
6 Trigonometric functions | |
7 Hyperbolic functions | |
8 Inverse hyperbolic and trigonometric functions | |
9 Quaternion matrices | |
10 Monomials, polynomials and binomials | |
11 Solutions | |
Bibliography | |
Index | |
ISBN: | 9783034806220 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Algebra , Functions of complex variables , Combinatorics , Geometry |
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Call number: | SPRINGER-2014-9783034805025:ONLINE Show nearby items on shelf |
Title: | Algebraic Methods in Functional Analysis [electronic resource] : The Victor Shulman Anniversary Volume |
Author(s): |
Ivan G Todorov Lyudmila Turowska |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This volume comprises the proceedings of the Conference on Operator Theory and its Applications held in Gothenburg, Sweden, April 26-29, 2011. The conference was held in honour of Professor Victor Shulman on the occasion of his65th birthday. The pape rs included in the volume covera large variety of topics, among them the theory of operator ideals, linear preservers, C*-algebras, invariant subspaces, non-commutative harmonic analysis, and quantum groups,andreflect recent developments in these areas. T he book consists of bothoriginal research papers and high quality survey articles, allofwhich werecarefully refereed |
Contents: | Introduction |
Victor Shulman: The Gentle Art of Mathematics | |
Operators Splitting the Arveson Spectrum | |
Singly Generated Operator Algebras Satisfying Weakened Versions of Amenability | |
Operator Algebras and C* | |
correspondences: A Survey | |
Some Operator Algebras from Semigroups | |
Lifting Algebraic Contractions in C* | |
algebras | |
The Second Local Multiplier Algebra of a Separable C* | |
algebra | |
Test | |
space Characterizations of Some Classes of Banach Spaces | |
Splittings of Masa | |
bimodules | |
Noncommutative Analogues of Stein Spaces of Finite Embedding Dimension | |
Idempotent States on Locally C | |
ISBN: | 9783034805025 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Operator Theory: Advances and Applications, 0255-0156 : v233 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Operator theory |
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Call number: | SPRINGER-2014-9781493912551:ONLINE Show nearby items on shelf |
Title: | The Corona Problem [electronic resource] : Connections Between Operator Theory, Function Theory, and Geometry |
Author(s): |
Ronald G Douglas Steven G Krantz Eric T Sawyer Sergei Treil Brett D Wick |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | The purpose of the corona workshop was toconsider the corona problem in both one and several complex variables, both in the context of function theory and harmonic analysis as well as the context of operator theory andfunctional analysis. It was held in June 2012 at the Fields Institute in Toronto, and attended by about fifty mathematicians. This volume validates and commemorates the workshop, and records some of the ideas that were developedwithin. The corona problem dates back to 1941. It has exert ed a powerful influence over mathematical analysis for nearly 75 years. There is material to help bring people up to speed in the latest ideas of the subject, as well ashistorical material to provide background. Particularly noteworthy is a history of the corona problem, authored by the five organizers, that provides a unique glimpse at how the problem and its many different solutions have developed.There has never been a meeting of this kind, and there has never been a volume of this kind. Mathematicians both veterans and newcomerswill benefit from reading this book. This volume makes a unique contribution to the analysisliterature and will be a valuable part of the canon for many years to come |
Contents: | The History of the Corona Problem (R.G. Douglas, S.G. Krantz, E.T. Sawyer, S. Treil, B.D. Wick) |
Corona Problem for H^\infty on Riemann Surfaces (A. Brudnyi) | |
Connections of the Corona Problem with Operator Theory and Complex Geometry (R.G. Douglas) | |
On the Maximal Ideal Space of a Sarason | |
Type Algebra on the Unit Ball (J. Eschmeier) | |
A Subalgebra of the Hardy Algebra Relevant in Control Theory and its Algebraic | |
Analytic Properties (M. Frentz, A. Sasane) | |
The Corona Problem in Several Complex Variables (S.G. Krantz) | |
Corona | |
Type Theorems and Division in Some Function Algebras on Pl | |
ISBN: | 9781493912551 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Fields Institute Communications, 1069-5265 : v72 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Functions of complex variables , Operator theory , Differential equations, partial |
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Call number: | SPRINGER-2014-9781493908080:ONLINE Show nearby items on shelf |
Title: | Optimization in Science and Engineering [electronic resource] : In Honor of the 60th Birthday of Panos M. Pardalos |
Author(s): |
Themistocles M Rassias Christodoulos A Floudas Sergiy Butenko |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Optimization in Science and Engineering is dedicated in honor of the 60th birthday of Distinguished Professor Panos M. Pardalos. Pardaloss past and ongoing work has made a significant impact on several theoretical and appliedareas in modern optimizat ion. As tribute to the diversity of Dr. Pardaloss work in Optimization, this book comprises a collection of contributions from experts in various fields of this rich and diverse area of science. Topicshighlight recent developments and include: Determinist ic global optimization Variational inequalities and equilibrium problems Approximation and complexity in numerical optimization Non-smooth optimization Statistical models and datamining Applications of optimization in medicine, energy systems, and complex network analysis This volume will be of great interest to graduate students, researchers, and practitioners, in the fields of optimization and engineering |
Contents: | Piecewise Linear Classifiers Based on Nonsmooth Optimization Approaches |
Variational Inequality Models Arising in the Study of Viscoelastic Materials | |
Neighboring Local Optimal Solutions and Its Applications | |
General Traffic Equilibrium Problem with Uncertainty and Random Variational Inequalities | |
Computational Complexities of Optimization Problems Related to Model Based Clustering of Networks | |
On Distributed | |
Lag Modeling Algorithms by r | |
Convexity and Piecewise Monotonicity | |
Poincar | |
Type Inequalities for Greens Operator on Harmonic Forms | |
The Robustness Concern in Preference | |
ISBN: | 9781493908080 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Software engineering , Computer science , Computer aided design , Mathematical optimization |
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Call number: | SPRINGER-2013-9789400760226:ONLINE Show nearby items on shelf |
Title: | Nonlinear Optical Properties of Materials [electronic resource] |
Author(s): |
Rashid A Ganeev |
Date: | 2013 |
Publisher: | Dordrecht : Springer Netherlands : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is mostly concerned on the experimental research of the nonlinear optical characteristics of various media, low- and high-order harmonic generation in different materials, and formation, and nonlinear opticalcharacterization of clusters. We also demonstrate the inter-connection between these areas of nonlinear optics. Nonlinear optical properties of media such as optical limiting can be applied in various areas of science andtechnology. To define suitable materials for these applications, o ne has to carefully analyse the nonlinear optical characteristics of various media, such as the nonlinear refractive indices, coefficients of nonlinear absorption,saturation absorption intensities, etc. Knowing the nonlinear optical parameters of material s is also important for describing the propagation effects, self-interaction of intense laser pulses, and optimisation of various nonlinearoptical processes. Among those processes one can admit the importance of the studies of the frequency conversion of coherent laser sources. The area of interest for nonlinear optical characterization of materials is also closelyrelated with new field of nanostructures formation and application during laser-matter interaction. We show how the nonlinear optical analysis of materials leads to improvement of their high-order nonlinear optical response during theinteraction with strong laser fields. Ablation-induced nanoparticles formation is correlated with their applications as efficient sources of coherent short-waveleng th photons. From other side, recent achievements of harmonic generationin plasmas are closely related with the knowledge of the properties of materials in the laser plumes. All of these studies are concerned with the low-order nonlinear optical features o f various materials. The novelty of the approachdeveloped in present book is related with inter-connection of those studies with each other |
Note: | Springer eBooks |
Contents: | Introduction |
References | |
Chapter 1 Low | |
order harmonic generation of laser radiation in various media | |
Chapter 2 High | |
order harmonic generation from laser ablation of various surfaces | |
Chapter 3 Nonlinear optical refraction and absorption of media | |
Chapter 4 Laser ablation induced cluster formation | |
Chapter 5 Low | |
order nonlinear optical characterization of clusters | |
Chapter 6 Application of nanoparticle | |
contained plasmas for high | |
order harmonic generation | |
ISBN: | 9789400760226 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Series in Optical Sciences, 0342-4111 : v174 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Optical materials |
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Call number: | SPRINGER-2013-9783642334061:ONLINE Show nearby items on shelf |
Title: | Invariant Random Fields on Spaces with a Group Action [electronic resource] |
Author(s): |
Anatoliy Malyarenko |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The author describes the current state of the art in the theory of invariant random fields. This theory is based on several different areas of mathematics, including probability theory, differential geometry, harmonic analysis,and special functions. The present volume unifies many results scattered throughout the mathematical, physical, and engineering literature, as well as itintroduces new results from this area first proved by the author. The book alsopresents many practical applications, in parti cular in such highly interesting areas as approximation theory, cosmology and earthquake engineering. It is intended for researchers and specialists working in the fields of stochasticprocesses, statistics, functional analysis, astronomy, and engineering. |
Note: | Springer eBooks |
Contents: | 1.Introduction |
2.Spectral Expansions | |
3.L2 Theory of Invariant Random Fields | |
4.Sample Path Properties of Gaussian Invariant Random Fields | |
5.Applications | |
A.Mathematical Background | |
References | |
Index | |
ISBN: | 9783642334061 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Probability and Its Applications, 1431-7028 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9783642326660:ONLINE Show nearby items on shelf |
Title: | Multi-Layer Potentials and Boundary Problems [electronic resource] : for Higher-Order Elliptic Systems in Lipschitz Domains |
Author(s): |
Irina Mitrea Marius Mitrea |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is ofsecond order a variety of t ools are available for dealing with such problems, including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. When thedifferential operator is of higher-order (as is the case, e .g., with anisotropic plate bending when one deals with a fourth order operator) only a few options could be successfully implemented. In the 1970s Alberto Caldern, one ofthe founders of the modern theory of Singular Integral Operators, advocated the use of layer potentials for the treatment of higher-order elliptic boundary value problems. The present monograph represents the first systematic treatmentbased on this approach. This research monograph lays, for the first time, the mathematical foundation ai med at solving boundary value problems for higher-order elliptic operators in non-smooth domains using the layer potential methodand addresses a comprehensive range of topics, dealing with elliptic boundary value problems in non-smooth domains including l ayer potentials, jump relations, non-tangential maximal function estimates, multi-traces and extensions,boundary value problems with data in WhitneyLebesque spaces, WhitneyBesov spaces, WhitneySobolev- based Lebesgue spaces, WhitneyTriebelLizorkin spaces, WhitneySobolev-based Hardy spaces, WhitneyBMO and WhitneyVMOspaces |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Smoothness scales and Calden | |
Zygmund theory in the scalar | |
valued case | |
3 Function spaces of Whitney arrays | |
4 The double multi | |
layer potential operator | |
5 The single multi | |
layer potential operator | |
6 Functional analytic properties of multi | |
layer potentials and boundary value problems | |
ISBN: | 9783642326660 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2063 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Integral equations , Differential equations, partial , Potential theory (Mathematics) |
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Call number: | SPRINGER-2013-9783319008493:ONLINE Show nearby items on shelf |
Title: | Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces [electronic resource] |
Author(s): |
Toka Diagana |
Date: | 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as wellas their recent gene ralizations. Some of the results presented are either new or else cannot be easily found in the mathematical literature. Despite the noticeable and rapid progress made on these important topics, the only standardreferences that currently exist on those ne w classes of functions and their applications are still scattered research articles. One of the main objectives of this book is to close that gap. The prerequisites for the book is the basicintroductory course in real analysis. Depending on the background of the student, the book may be suitable for a beginning graduate and/or advanced undergraduate student. Moreover, it will be of a great interest to researchers inmathematics as well as in engineering, in physics, and related areas. Further, some parts o f the book may be used for various graduate and undergraduate courses |
Note: | Springer eBooks |
Contents: | 1. Metric, Banach, and Hilbert Spaces |
2. Linear Operators on Banach Spaces | |
3. Almost Periodic Functions | |
4. Almost Automorphic Functions | |
5. Pseudo | |
Almost Periodic Functions | |
6. Pseudo | |
Almost Automorphic Functions | |
7. Existence Results for Some Second | |
Order Differential Equations | |
8. Existence Results to Some Integrodifferential Equations | |
9. Existence of C(m) | |
Pseudo | |
Almost Automorphic Solutions | |
10. Pseudo | |
Almost Periodic Solutions to Some Third | |
Order Differential Equations | |
11. Pseudo | |
Almost Automorphic Solutions to Some Sobolev | |
Type Equations | |
12. Stability Results f | |
ISBN: | 9783319008493 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Operator theory , Differential Equations , Differential equations, partial |
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Call number: | SPRINGER-2013-9783319007595:ONLINE Show nearby items on shelf |
Title: | Beam Diagnostics in Superconducting Accelerating Cavities [electronic resource] : The Extraction of Transverse Beam Position from Beam-Excited Higher Order Modes |
Author(s): |
Pei Zhang |
Date: | 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This workemploys self-excited wakefields as a diagnostic to remotely determine the beam position within a superconducting cavity and chains thereof. Several numerical techniques are delineated in order to ascertain the mostappropriate technique in te rms of reliability and accuracy. The methodologyis carefully explainedmaking the presentation pedagogically appropriate to students new to the field as well asresearchers familiar with this topic.PeiZhang'sachievementswill serve as a basis for the develop ment of similar monitors at various other facilities around the world |
Note: | Springer eBooks |
Contents: | Electromagnetic Eigenmode Simulations of the Third Harmonic Cavity |
Measurements of HOM Spectra | |
Analysis Methods for Beam Position Extraction from HOM | |
Dependencies of HOM on Transverse Beam Offsets | |
HOM | |
Based Beam Position Diagnostics | |
ISBN: | 9783319007595 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5053 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Particle acceleration |
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Call number: | SPRINGER-2013-9783319001289:ONLINE Show nearby items on shelf |
Title: | Hypoelliptic Laplacian and BottChern Cohomology [electronic resource] : A Theorem of RiemannRochGrothendieck in Complex Geometry |
Author(s): |
Jean-Michel Bismut |
Date: | 2013 |
Publisher: | Heidelberg : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of RiemannRochGrothendieck for proper submersions. It gives an equality of cohomology classes inBottChern cohomology, which is a refi nement for complex manifolds of de Rham cohomology. When the manifolds are Khler, our main result is known. A proof can be given using the elliptic Hodge theory of the fibres, its deformationvia Quillen's superconnections, and a version in families of the 'fantastic cancellations' of McKeanSinger in local index theory. In the general case, this approach breaks down because the cancellations do not occur any more.Onetool used in the book is a deformation of the Hodge theory of the fibres to a hypoelliptic Hodge theory, in such a way that the relevant cohomological information is preserved, and 'fantastic cancellations' do occur for thedeformation. The deformed hypoelliptic Laplacian acts on the total space of the relative tangent bundle of the fibres. Whil e the original hypoelliptic Laplacian discovered by the author can be described in terms of the harmonicoscillator along the tangent bundle and of the geodesic flow, here, the harmonic oscillator has to be replaced by a quartic oscillator.Another idea dev eloped in the book is that while classical elliptic Hodge theory is based on theHermitian product on forms, the hypoelliptic theory involves a Hermitian pairing which is a mild modification of intersection pairing. Probabilistic considerations play an imp ortant role, either as a motivation of some constructions,or in the proofs themselves |
Note: | Springer eBooks |
Contents: | Introduction |
1 The Riemannian adiabatic limit | |
2 The holomorphic adiabatic limit | |
3 The elliptic superconnections | |
4 The elliptic superconnection forms | |
5 The elliptic superconnections forms | |
6 The hypoelliptic superconnections | |
7 The hypoelliptic superconnection forms | |
8 The hypoelliptic superconnection forms of vector bundles | |
9 The hypoelliptic superconnection forms | |
10 The exotic superconnection forms of a vector bundle | |
11 Exotic superconnections and RiemannRochGrothendieck | |
Bibliography | |
Subject Index | |
Index of Notation. | |
ISBN: | 9783319001289 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v305 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , K-theory , Global analysis , Differential equations, partial |
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Title: | Offbeat Integral Geometry on Symmetric Spaces [electronic resource] |
Author(s): |
Valery V Volchkov Vitaly V Volchkov |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces ofarbitrary ranks as we ll as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for variousclasses of functions, far-reaching generalizatio ns of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful invarious fields of contemporary mathematics. The proofs given are mini mal in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historicalperspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and theHeisenberg group, integral equations, special functions, and transmutation operators theory |
Note: | Springer eBooks |
Contents: | Preface |
Part 1. Analysis on Symmetric Spaces. 1 Preliminaries | |
2 The Euclidean case | |
3 Symmetric spaces of the non | |
compact type | |
4 Analogies for compact two | |
point homogeneous Spaces | |
5 The phase space associated to the Heisenberg group | |
Part 2. Offbeat Integral Geometry | |
1 Functions with zero ball means on Euclidean space | |
2 Two | |
radii theorems in symmetric spaces | |
3 The problem of finding a function from its ball means | |
4 Sets with the Pompeiu property | |
5 Functions with zero integrals over polytopes | |
6 Ellipsoidal means | |
7 The Pompeiu property on a sphere | |
8 The Pompeiu | |
ISBN: | 9783034805728 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Integral Transforms , Functions, special , Global differential geometry |
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Call number: | SPRINGER-2013-9783034805636:ONLINE Show nearby items on shelf |
Title: | Special Functions of Mathematical (Geo-)Physics [electronic resource] |
Author(s): |
Willi Freeden Martin Gutting |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A goodunderstanding of special fun ctions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The specialfunctions to be discussed in this monograph vary great ly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective fieldcharacteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercisesthat reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields ofresearch, where special functions are essential to application. All in all, the book is an equally valuable resource for educa tion in geomathematics and the study of applied and harmonic analysis. Students who wish to continue withfurther studies should consult the literature given as supplements for each topic covered in the exercises |
Note: | Springer eBooks |
Contents: | 1 Introduction: Geomathematical Motivation |
Part I: Auxiliary Functions | |
2 The Gamma Function | |
3 Orthogonal Polynomials | |
Part II: Spherically Oriented Functions | |
4 Scalar Spherical Harmonics in R^3 | |
5 Vectorial Spherical Harmonics in R^3 | |
6 Spherical Harmonics in R^q | |
7 Classical Bessel Functions | |
8 Bessel Functions in R^q | |
Part III: Periodically Oriented Functions | |
9 Lattice Functions in R | |
10 Lattice Functions in R^q | |
11 Concluding Remarks | |
References | |
Index | |
ISBN: | 9783034805636 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Physical geography , Meteorology , Harmonic analysis , Differential equations, partial , Functions, special |
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Call number: | SPRINGER-2013-9783034805483:ONLINE Show nearby items on shelf |
Title: | Variable Lebesgue Spaces [electronic resource] : Foundations and Harmonic Analysis |
Author(s): |
David V Cruz-Uribe Alberto Fiorenza |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They wereintroduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, andfor their applications to problems in physics and ima ge processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-onapproach that makes clear the similarities and differences between the vari able and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewoodmaximal operator is completely developed, and the connections between variable Lebesguespaces and t he weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Rieszpotentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolatio n from the theory of weighted norm inequalities. The final chapter applies the results from previouschapters to prove basic results about variable Sobolev spaces |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Structure of Variable Lebesgue Spaces | |
3 The Hardy | |
Littlewood Maximal Operator | |
4 Beyond Log | |
Hlder Continuity | |
5 Extrapolation in the Variable Lebesgue Spaces | |
6 Basic Properties of Variable Sobolev Spaces | |
Appendix: Open Problems | |
Bibliography | |
Symbol Index | |
Author Index | |
Subject Index. | |
ISBN: | 9783034805483 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Global analysis |
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Call number: | SPRINGER-2013-9783034805377:ONLINE Show nearby items on shelf |
Title: | Operator Theory, Pseudo-Differential Equations, and Mathematical Physics [electronic resource] : The Vladimir Rabinovich Anniversary Volume |
Author(s): |
Yuri I Karlovich Luigi Rodino Bernd Silbermann Ilya M Spitkovsky |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume is a collection of papers devoted to the 70th birthday of Professor Vladimir Rabinovich. The opening article (by Stefan Samko) includes a short biography and the bibliography of Vladimir Rabinovichs works, alongwith personal recollections . It is followed by twenty research and survey papers in various branches of analysis (pseudodifferential operators and partial differential equations, Toeplitz, Hankel, and convolution type operators,variable Lebesgue spaces, etc.) close to Professor Rab inovichs research interests. Many of them are written by participants of the international workshop Analysis, Operator Theory, and Mathematical Physics (Ixtapa, Mexico,January 2327, 2012), who have a long history of scientific collaboration with Rabinovic h and whose contributions are partially based on the talks presented at that meeting. The volume will be of great interest to researchers andgraduate students working in the fields of differential equations, operator theory, functional and harmonic analys is and mathematical physics |
Note: | Springer eBooks |
Contents: | Preface |
Contributions by renowned scientists | |
References | |
ISBN: | 9783034805377 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v228 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Operator theory , Differential equations, partial |
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Call number: | SPRINGER-2013-9783034805346:ONLINE Show nearby items on shelf |
Title: | Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields [electronic resource] |
Author(s): |
Yuan-Jen Chiang |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Harmonic maps between Riemannian manifolds were first established in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals ofconnections whose cur vature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introducedin 1986. The book presents an overview of the important developmentsmadein these fields since they first came up. Furthermore,it introduces biwave maps (generalizing wave maps) which were first studiedin 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated in 2008.Other topicsdiscussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields |
Note: | Springer eBooks |
Contents: | Preface. 1 Harmonic Maps |
2 Wave Maps | |
3 Yang | |
Mills Fields | |
4 Biharmonic Maps | |
5 Biwave Maps | |
6 Bi | |
Yang | |
Mills Fields | |
7 Exponential Harmonic Maps | |
8 Exponential Wave Maps | |
9.Exponential Yang | |
Mills Connections | |
Index. | |
ISBN: | 9783034805346 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Frontiers in Mathematics, 1660-8046 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Differential equations, partial , Global differential geometry , Mathematical optimization |
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Call number: | SPRINGER-2013-9783034805162:ONLINE Show nearby items on shelf |
Title: | Advances in Harmonic Analysis and Operator Theory [electronic resource] : The Stefan Samko Anniversary Volume |
Author(s): |
Alexandre Almeida Lus Castro Frank-Olme Speck |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume is dedicated to Professor Stefan Samko on the occasion of his seventieth birthday. The contributions display the range of his scientific interests in harmonic analysis and operator theory. Particular attentionispaidto fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well asrelatedapplications, to mention but a few. Most of the contributions were originally presented at two conferences in Lisbon and Aveiro, Portugal, in JuneJuly 2011 |
Note: | Springer eBooks |
ISBN: | 9783034805162 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v229 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Operator theory , Potential theory (Mathematics) |
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Call number: | SPRINGER-2013-9783034804691:ONLINE Show nearby items on shelf |
Title: | Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals [electronic resource] |
Author(s): |
Sergey Kislyakov Natan Kruglyak |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In this book we suggest a unified method of constructing near-minimizers for certain important functionals arising in approximation, harmonic analysis and ill-posed problems and most widely used in interpolation theory. Theconstructions are based on far-reaching refinements of the classical CaldernZygmund decomposition. These new CaldernZygmund decompositions in turn are produced with the help of new covering theorems that combine manyremarkable features of classical resultsestablished byBesicovitch, Whitney and Wiener. In many cases the minimizers constructed in the book are stable (i.e., remain near-minimizers) under the action of CaldernZygmund singularintegral operators. The book is divided into two parts. While the new method is presented in gre at detail in the second part, the first is mainly devoted to the prerequisites needed for a self-contained presentation of the main topic.There we discuss the classical covering results mentioned above, various spectacular applications of the classical Ca ldernZygmund decompositions, and the relationship of all this to real interpolation. It also serves as a quickintroduction to such important topics as spaces of smooth functions or singular integrals |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Definitions, notation, and some standard facts | |
Part 1. Background | |
Chapter 1. Classical CaldernZygmund decomposition and real interpolation | |
Chapter 2. Singular integrals | |
Chapter 3. Classical covering theorems | |
Chapter 4. Spaces of smooth functions and operators on them | |
Chapter 5. Some topics in interpolation | |
Chapter 6. Regularization for Banach spaces | |
Chapter 7. Stability for analytic Hardy spaces | |
Part 2. Advanced theory | |
Chapter 8. Controlled coverings | |
Chapter 9. Construction of near | |
minimizers | |
Chapter 10. Stability of near | |
mini | |
ISBN: | 9783034804691 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Monografie Matematyczne : v74 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis |
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Call number: | SPRINGER-2013-9781461487814:ONLINE Show nearby items on shelf |
Title: | Ricci Flow for Shape Analysis and Surface Registration [electronic resource] : Theories, Algorithms and Applications |
Author(s): |
Wei Zeng Xianfeng David Gu |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Ricci Flow for Shape Analysis and Surface Registration introduces the beautiful and profound Ricci flow theory in a discrete setting. By using basic tools in linear algebra and multivariate calculus, readers can deduce all themajor theorems in surfac e Ricci flow by themselves. The authors adapttheRicci flow theory to practical computational algorithms, apply Ricci flow for shape analysis and surface registration, and demonstrate the power of Ricciflow in many applications in medical imaging, computer graphics, computer vision and wireless sensor network. Due to minimal pre-requisites, this bookis accessible toengineersand medicalexperts, including educators,researchers, students and industry engineerswhohave an interest insolvingreal problems related to shape analysis and surface registration. |
Note: | Springer eBooks |
Contents: | 1. Introduction |
2. Computational | |
3.Computational Geometry | |
4. Differential Geometry of Surface | |
5. Riemann Surface | |
6. Ricci Flow | |
7. Topological Algorithms | |
8. Harmonic Maps | |
9. Discrete Ricci Flow | |
10. Shape Analysis | |
11. Surface Diffeomorphism | |
12. Medical Imaging Applications | |
13. Computer Vision Applications | |
14. Computer Graphics Applications | |
15. Network Applications. | |
ISBN: | 9781461487814 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer vision , Computer science Mathematics , Geometry , Discrete groups |
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Call number: | SPRINGER-2013-9781461485261:ONLINE Show nearby items on shelf |
Title: | Hermitian Analysis [electronic resource] : From Fourier Series to Cauchy-Riemann Geometry |
Author(s): |
John P D'Angelo |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry provides a coherent, integrated look at various topics from analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transformon the real line, an d then turns to the heart of the book: geometric considerations in several complex variables. The final chapter includes complex differential forms, geometric inequalities from one and several complex variables,finite unitary groups, proper mappings, and naturally leads to the Cauchy-Riemann geometry of the unit sphere. The book thus takes the reader from the unit circle to the unit sphere. This textbook will be a useful resource forupper-undergraduate students who intend to continue with mathematics, gra duate students interested in analysis, and researchers interested in some basic aspects of CR Geometry. It will also be useful for students in physics andengineering, as it includes topics in harmonic analysis arising in these subjects.The inclusion of an appendix and more than 270 exercises makes this book suitable for a capstone undergraduate Honors class |
Note: | Springer eBooks |
Contents: | Preface |
Introduction to Fourier series | |
Hilbert spaces | |
Fourier transform on R | |
Geometric considerations | |
Appendix | |
References | |
Index. | |
ISBN: | 9781461485261 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Cornerstones, 2197-182X |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Differential Equations , Global differential geometry |
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Call number: | SPRINGER-2013-9781461482086:ONLINE Show nearby items on shelf |
Title: | Distributions, Partial Differential Equations, and Harmonic Analysis [electronic resource] |
Author(s): |
Dorina Mitrea |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. Thebook is written in a for mat suitable for a graduate course spanning either over one-semester, when the focus is primarily on the foundational aspects, or over a two-semester period that allows for the proper amount of time to coverall intended applications as well. It presents a balanced treatment of the topics involved, and contains a large number of exercises (upwards of two hundred, more than half of which are accompanied by solutions), which have beencarefully chosen to amplify the effect, and substantiate the power and scop e, of the theory of distributions. Graduate students, professional mathematicians, and scientifically trained people with a wide spectrum of mathematicalinterests will find this book to be a useful resource and complete self-study guide. Throughout, a spe cial effort has been made to develop the theory of distributions not as an abstract edifice but rather give the reader a chance tosee the rationale behind various seemingly technical definitions, as well as the opportunity to apply the newly developed too ls (in the natural build-up of the theory) to concrete problems in partial differential equations and harmonicanalysis, at the earliest opportunity |
Note: | Springer eBooks |
Contents: | Introduction |
Summary of Topological and Functional Analysis Results | |
Weak Derivatives | |
The Space D0() of Distributions | |
The Fourier Transform | |
The Space of Tempered Distributions | |
Fundamental Solution | |
The Laplace Operator | |
The Heat Operator | |
The Wave Operator | |
The Lame Operator | |
Fundamental Solutions for Other Operators | |
Hypoelliptic operators | |
Sobolev spaces | |
Appendix | |
References. | |
ISBN: | 9781461482086 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functional analysis , Differential equations, partial , Potential theory (Mathematics) |
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Call number: | SPRINGER-2013-9781461479727:ONLINE Show nearby items on shelf |
Title: | Harmonic Analysis on Symmetric SpacesEuclidean Space, the Sphere, and the Poincar Upper Half-Plane [electronic resource] |
Author(s): |
Audrey Terras |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincar upper half plane. This book is intended for beginning graduate students inmathematics or researchers in phy sics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, andengineering. Many corrections, new topics, and updates have be en incorporated in this new edition. These include discussions of the work of P. Sarnak and others making progress on various conjectures on modular forms, the work of T.Sunada, Marie-France Vignras, Carolyn Gordon, and others on Mark Kac's question Can y ou hear the shape of a drum?, Ramanujan graphs, wavelets, quasicrystals, modular knots, triangle and quaternion groups, computations of Maasswaveforms, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summationformula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon tr ansform, non-Euclidean geometry on the Poincar upper half plane H or unit disc andapplications to microwave engineering, fundamental domains in H for discrete groups , tessellations of H from such discrete group actions, automorphic forms, the Selberg tra ce formula and its applications in spectral theory as wellas number theory |
Note: | Springer eBooks |
Contents: | Chapter1 Flat Space. Fourier Analysis on R^m |
1.1 Distributions or Generalized Functions | |
1.2 Fourier Integrals | |
1.3 Fourier Series and the Poisson Summation Formula | |
1.4 Mellin Transforms, Epstein and Dedekind Zeta Functions | |
1.5 Finite Symmetric Spaces, Wavelets, Quasicrystals, Weyls Criterion for Uniform Distribution | |
Chapter2 A Compact Symmetric Space | |
The Sphere | |
2.1 Fourier Analysis on the Sphere | |
2.2 O(3) and R^3. The Radon Transform | |
Chapter 3 The Poincar Upper Half | |
Plane | |
3.1 Hyperbolic Geometry | |
3.2 Harmonic Analysis on H | |
3.3 Fundamental Domains for | |
ISBN: | 9781461479727 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Topological Groups , Harmonic analysis , Fourier analysis , Functions of complex variables , Functions, special |
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Call number: | SPRINGER-2013-9781461479246:ONLINE Show nearby items on shelf |
Title: | Geometric Analysis of the Bergman Kernel and Metric [electronic resource] |
Author(s): |
Steven G Krantz |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties,boundary asymptotics, an d asymptotic expansion of the Bergman kernel and metric.Moreover, itpresents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretationsin the language of functional analysis, with emp hasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection ofexercises which will be of interest to both graduate students and experienc ed mathematicians. Graduate students who have taken courses in complex variables and have a basic background in real and functional analysis will find thistextbook appealing. Applicable courses for either main or supplementary usage include those in compl ex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complexanalysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the man y exciting aspects of Bergman's theory |
Note: | Springer eBooks |
Contents: | Preface |
1. Introductory Ideas | |
2.The Bergman Metric | |
3. Geometric and Analytic Ideas | |
4. Partial Differential Equations | |
5. Further Geometric Explorations | |
6. Additional Analytic Topics | |
7. Curvature of the Bergman Metric | |
8. Concluding Remarks | |
Table of Notation | |
Bibliography | |
Index | |
ISBN: | 9781461479246 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v268 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Differential equations, partial , Global differential geometry |
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Location: | ONLINE |
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