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SPIRES-BOOKS: FIND KEYWORD FOURIER ANALYSIS *END*INIT* use /tmp/qspiwww.webspi1/21883.50 QRY 131.225.70.96 . find keyword fourier analysis ( in books using www Cover
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Call number:9783319444314:ONLINE Show nearby items on shelf
Title:Interferometry and Synthesis in Radio Astronomy
Author(s): A. Richard Thompson
Date:2017
Edition:3rd ed. 2017
Size:1 online resource (XLVI, 872 p. 252 illus., 10 illus. in color p.)
Contents:Preface -- Introduction and Historical Review -- Introductory Theory of Interferometry and Synthesis Imaging -- Analysis of the Interferometer Response -- Geometric Relationships and Polarimetry -- Antennas and Arrays -- Response of
the Receiving System -- Design of the Analog Receiving System -- Digital Signal Processing -- Very-Long-Baseline Interferometry -- Calibration and Fourier Transformation of Visibility Data -- Deconvolution, Adaptive Calibration and
Applications -- Interferometer Techniques for Astrometry and Geodesy -- Propagation Effects -- Van Cittert-Zernike Theorem, Spatial Coherence and Scattering -- Radio Interference -- Related Techniques -- Principal Symbols -- Index
ISBN:9783319444314
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Physics , Observations, Astronomical , Astronomy , Physics , Astronomy, Observations and Techniques , Applied and Technical Physics
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Call number:9781608077779:ONLINE Show nearby items on shelf
Title:Terahertz metrology
Author(s): Mira Naftaly
Date:2015
Publisher:Artech House
Size:1 online resource (386 p.)
Contents:Chapter 1 Terahertz Time-Domain Spectrometers -- Photoconductive Emitters and Detectors -- Optical Rectification -- Electro-Optic Detection -- Terahertz Air-Based Coherent Detection -- Cherenkov (Tilted Wavefront) Emitters and Detectors -- Continuou s-Wave Terahertz Time-Domain Spectrometer and Microwave Photonics -- Types of Continuous-Wave Terahertz Emitters and Detectors -- Time-Domain Spectrometer Configurations -- Transmission -- Reflection -- Attenuated Total Reflection -- Asynchronous Optical Sampling -- Substrate Lenses -- Commercial Systems -- Parameter Extraction in Time-Domain . Chapter 2 Spectrometers -- Material Properties and Wave Propagation -- Complex Refractive Index and Complex Permittivity -- Plane Wave Propagation Across an Interf ace.Fresnel Equations -- Plane Wave Propagation Through a Dielectric Slab -- Fabry-Perot Effect -- Extracting Optical Parameters from Terahertz Time-Domain Spectrometers Data -- Transmission-mode Terahertz Time-Domain Spectrometers: Approximation -- Trans mission-Mode Terahertz Time-Domain Spectrometers: Exact Solution -- Reflection-Mode Terahertz Time-Domain Spectrometers: Single Reflection -- Reflection-Mode Terahertz Time-Domain Spectrometers: Double Reflection -- Attenuated Total Reflection -- Preproce ssing and Postprocessing of Data -- Signal Averaging in the Time and Frequency Domains -- Signal Denoising -- Phase Unwrapping -- Sample Requirements -- Sample Thickness -- Lateral Dimensions of Samples -- Loss: Absorption, Scattering, Diffraction
Chapter 3 Metrology for Time-Domain Spectrometers -- Performance Parameters: Sensitivity, Resolution, Precision, Accuracy, Dynamic Range, and Signal-to-Noise Ratio -- Dynamic Range and Signal-to-Noise Ratio of Terahertz Time-Domain Spectrometers -- System Performance Limits Due to Dynamic Range and Signal-to-Noise Ratio -- Frequency Resolution -- Measurement Bandwidth -- Sources of Random Noise -- Amplitude -- Phase -- Systematic Errors -- Alignment Errors -- Focal Plane Defocusing -- Delay Line Err ors -- Terahertz Beam Profile -- Chapter 4 Evaluation of Uncertainty in Time-Domain Spectroscopy -- Method of Uncertainty Evaluation -- Evaluation of Random and Systematic Errors -- Propagation and Combination of Measurement Uncertainty -- Measurement wit h Resolution Limit -- Sources of Uncertainty in Terahertz Time-Domain Spectroscopy -- Random and Systematic Errors in Amplitude -- Random and Systematic Errors in Sample Thickness -- Random and Systematic Errors in Sample Alignment -- Systematic Error in the Approximated Transfer Function -- Systematic Error Due to Reflections -- Systematic Error in Physical Constants -- Uncertainty in Optical Constants: A Combination of Variances
Chapter 5 Metrology for Fourier Transform Spectrometers -- Spectrometer Configurations -- Michelson -- Mach-Zender -- Polarized Fourier Transform Spectrometer (Martin-Pupplett Interferometer) -- Modes of Operation: Step and Integrate or Fast Scannin g -- Moving Stage -- General Fourier Transform Spectrometer Advantages -- Fourier Transform Spectrometer Metrology -- Encoders, Synchronizing, and Time-Stamping -- Instrument Line Function: A Spectral Resolution Limitation -- Apodization -- Cosine and Sin e Terms and Phase Correction Techniques -- Achievable Spectral Resolution -- Sample Measurement Parameter Recovery -- Thin Sample Approximation: Lossless Case -- Dispersive Medium -- Thick Sample Analysis (or Noncollimated Measurement) -- Absorption Coeff icients -- Sources of Noise and Uncertainties -- Time-Domain Errors -- (Software) Noise Reduction Techniques -- Chapter 6 Terahertz Spectrometer Calibration -- Why Calibrate Terahertz Spectrometers -- Frequency Calibration -- Gases -- Solids -- Resonant M esh Filters -- Etalons -- Summary of Frequency Calibration Standards -- Amplitude Linearity Calibration -- Reflection Standards
Chapter 7 Terahertz Imaging -- Image Resolution of a Terahertz Imaging System -- Data Analysis in the Far Field -- Imaging Thin Layers -- Spatial Resolution Tests -- Near-Field Imaging -- Chemical Imaging -- Focal Plane Array Microbolometer Cameras -- Chapter 8 Metrology for Vector Network Analyzers -- Vector Network Analyzers -- The Role of a Network Analyzer -- Scattering Parameters -- Vector Network Analyzer Systems -- Extender Heads -- Good Practice Tips -- Metallic Waveguides -- Basic Properti es -- Dispersion -- Standardized Sizes and Frequency Ranges -- Flanges/Interfaces -- Good Practice Tips -- Calibration Standards and Methods -- Calibration: General Principles -- Types of Calibration Standard -- One-Port Calibration Methods -- Two-Port Ca libration Methods -- Connection Repeatability -- System Verification -- Chapter 9 Terahertz Optics -- Terahertz Optical Materials -- Transparency at Terahertz Frequencies -- Inorganic Crystals for Terahertz Optics -- Polymers for Terahertz Optics -- Metal Reflectivities -- Gaussian Optics -- Gaussian Beams -- Parabolic Mirrors -- Dichroic Optical Elements -- Terahertz Transparent/Visible Opaque -- Terahertz Opaque/Visible Transparent -- Terahertz Reflective/Visible Transparent -- Terahertz Transparent/Vis ible Reflective -- Wire-Grid Polarizers -- Antireflection Coatings -- Photonic Crystal Fibers and Terahertz . Waveguides
Chapter 10 Terahertz Laser Sources -- Optically Pumped Gas Lasers -- P-Germanium Laser -- Quantum Cascade Lasers -- Pulsed Difference Frequency Generation -- High-Resolution Frequency Measurements Using Continuous-Wave Difference Frequency Generatio n -- Optical Parametric Oscillators -- Free Electron Lasers -- Chapter 11 Electronic Sources of Terahertz Radiation and Terahertz Detectors -- Electronic Sources of Terahertz Radiation: Introduction and Terminology -- Vacuum Electronic Sources -- Backward Wave Oscillators -- Extended Interaction Klystrons -- Solid-State Devices -- Gunn Diodes and IMPATT Oscillators and Amplifiers -- Transistor Amplifiers -- Frequency Multiplied Sources -- Source Characteristics Summary -- Detectors of Terahertz Radiation: Introduction and Terminology . Incoherent Detectors -- Golay Cell -- Pyroelectric Detectors -- Room-Temperature Bolometers -- Cryogenic Bolometers -- Photoconductive Detectors -- Semiconductor Diode Rectifiers -- Thermopiles -- Incoherent Detector Summar y -- Coherent Detectors: Introduction -- Schottky Diode Mixers -- Frequency Measurement
ISBN:9781608077762
Series:eBooks
Series:Artech ebooks
Keywords: Terahertz spectroscopy. , Metrology. , Terahertz technology.
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Call number:9781608075355:ONLINE Show nearby items on shelf
Title:Microstrip lines and slotlines
Author(s): Ramesh Garg
I. J. Bahl
Maurizio Bozzi
Date:2013
Edition:Third edition.
Publisher:Artech House
Size:1 online resource (589 p.)
Contents:Chapter 1 Microstrip Lines I - Quasi-Static Analyses, Dispersion Models, and Measurements -- Planar Transmission Structures -- Microstrip Field Configuration -- Methods of Microstrip Analysis Quasi-Static Analyses of a Microstrip -- Modified Conformal Transformation Method -- Finite Difference Method -- Integral Equation Meth od -- Variational Method in the Fourier Transform Domain -- Segmentation and Boundary Element Method -- Microstrip Dispersion Models -- Coupled TEM Mode and TM Mode Model -- An Empirical Relation -- Dielectric-Loaded Ridged Waveguide Model -- Empirical F ormulae for Broad Frequency Range -- Planar Waveguide Model -- Microstrip Transitions -- Coaxial-to-Microstrip Transition -- Waveguide-to-Microstrip Transition -- Microstrip Measurements -- Substrate Dielectric Constant -- Characteristic Impendance -- Pha se Velocity or Effective Dielectric Constant -- Attenuation Constant -- Fabrication -- Printed Circuit Technologies -- Hybrid Microwave Integrated Circuits -- Monolithic Integrated Circuit Technologies
Chapter 2 Microstrip Lines II -- Fullwave Analyses, Design Considerations, and Applications -- Methods of Fullwave Analysis -- Analysis of an Open Microstrip -- Integral Equation Method in the Space Domain -- Galerkin.s Method in the Spectral Domain -- Analysis of an Enclosed Microstrip -- Integral Equation Methods -- Finite Difference Method -- Design Considerations -- Microstrip Losses -- Power Handling Capability -- Effect of Tolerances -- Effect of Dielectric Anisotropy -- Frequency Range of Ope ration -- Lumped Element Model of Microstrip Interconnect -- Other Types of Microstrip Lines -- Suspended and Inverted Microstrip Lines -- Multilayered Dielectric Microstrip -- Thin Film Microstrip -- Valley Microstrip Lines -- Buried Microstrip Line -- S uperconducting Microstrip Circuits -- Microstrip Applications -- Lumped Elements -- Passive Components -- Active Components -- Packages and Assemblies
Chapter 3 Microstrip Discontinuities I -- Quasi-Static Analysis and Characterization -- Discontinui ty Capacitance Evaluation -- Matrix Inversion Method -- Variational Method -- Galerkins Method in the Fourier Transform Domain -- Use of Line Sources with Charge Reversal -- Discontinuity Inductance Evaluation -- Characterization of Various Discontinuitie s -- Open Ends -- Gaps in a Microstrip -- T-Junctions -- Cross Junctions -- RF Short and Via Hole -- Compensated Microstrip Discontinuities
Chapter 4 Microstrip Discontinuities II: Fullwave Analysis and Measurements -- Planar Waveguide Analysis -- Discontinuity Characterization -- Compensation of Discontinuity Reactances -- Radiation and Parasitic Coupling -- Fullwave Analysis of Discon tinuities . Galerkins Method in the Spectral Domain -- Integral Equation Solution in the Space Domain -- Time Domain Methods for Microstrip Discontinuity -- Discontinuity Measurements -- Linear Resonator Method -- Ring Resonator Method -- Scattering Param eters Measurement Method
Chapter 5 Slotlines -- Slotline Analysis -- Approximate Analysis -- Transverse Resonance Method . Galerkins Method in the Spectral Domain -- Design Considerations -- Closed-Form Expressions -- Effect of Metal Thickness -- Effec t of Tolerances -- Losses in Slotline -- Slotline Discontinuities -- Short End Discontinuty -- Open End Discontinuity -- Variants of Slotline -- Coupled Microstrip-Slotline -- Conductor-Backed Slotline -- Conductor-Backed Slotline with Superstrate -- Slot lines with Double-Layered Dielectric -- Slotline Transitions -- Coaxial-to-Slotline Transition -- Microstrip-to-Slotline Cross-Junction Transition -- Slotline Applications -- Circuits Using T-Junctions -- Circuits Using Wideband 180 Phase Shift -- Hybrid /de Ronde.s Branchline Couplers
Chapter 6 Defected Ground Structure (DGS) -- Basic Structure of DGS -- Unit Cell and Periodic DGS -- Advantages and Disadvantages of DGS -- DGS Characteristics -- Stop-Band Properties -- Slow-Wave Propagation -- Realization of Transmission Lines wit h High Characteristic Impedance -- Modeling of DGS -- Full-Wave Modeling -- Equivalent Circuit Models -- Applications of DGS -- DGS-Based Filters -- Other DGS-Based Passive Components -- DGS-Based Active Circuits -- DGS-Based Antennas
Chapter 7 Coplan ar Lines: Coplanar Waveguide and Coplanar Strips -- Quasi-Static Conformal Mapping Analysis of CPW -- Quasi-Static Conformal Mapping Analysis of CPS -- Fullwave Analysis -- Design Considerations -- Design Equations -- Dispersion -- Effect of Metallization Thickness -- Losses in Coplanar Lines -- Dielectric Loss -- Conductor Loss -- Radiation and Surface Wave Losses -- Effect of Tolerances -- Comparison with Microstrip Line and Slotline -- Transitions -- Coax-to-CPW Transitions -- Microstrip-to-CPS Transit ions -- Microstrip-to-CPW Transition -- CPW-to-CPS Transitions -- CPS-to-Slotline Transitions -- Slotline-to-CPW Transitions -- Discontinuities in Coplanar Lines -- CAD Models for Discontinuities in Coplanar Waveguide Circuits -- CAD Models for Discontinu ities in Coplanar Strips Circuits -- Coplanar Line Circuits -- Circuits with Series and Shunt Reactances in CPW -- Circuits Using Slotline-CPW Junctions
Chapter 8 Coupled Microstrip Lines -- General Analysis of Coupled Lines -- Methods of Analysis -- Coupled Mode Approach -- Even- and Odd-Mode Approach -- Characteristics of Coupled Microstrip Lines -- Quasi-Static Analysis -- Fullwave Analysis -- Di spersion Models -- Measurements on Coupled Microstrip Lines -- Impedance Measurements -- Phase Constant Measurements -- Design Considerations for Coupled Microstrip Lines -- Design Equations -- Effect of Fabrication Tolerances -- Coupled Microstrip Lines with Dielectric Overlays -- Effect of Dielectric Anisotropy -- Slot-Coupled Microstrip Lines -- Coupled Multiconductor Microstrip Lines -- Discontinuities in Coupled Microstrip Lines -- Network Model -- Open-End Discontinuity
Chapter 9 Substrate Integrated Waveguide (SIW) -- Operation Principle -- Analysis Techniques of SIW . Equivalent Rectangular Waveguide -- Full-wave Modeling of SIW Interconnects -- Full-wave Modeling of SIW Components -- Equivalent Circuits Models o f SIW Discontinuities -- Design Considerations -- Mechanisms of Loss -- Guided.wave and Leaky-wave Regions of Operation -- Band-gap Effects in SIW Structures -- SIW Design Rules -- Substrate Integrated Folded Waveguide (SIFW) -- Half-Mode Substrate Integr ated Waveguide (HMSIW) -- Substrate Integrated Slab Waveguide (SISW) -- Substrate Integrated Ridge Waveguide (SIRW) -- Transitions Between SIW and Planar Transmission Lines -- Microstrip-to-SIW Transitions -- CPW-to-SIW Transitions -- SIW Components and A ntennas -- Passive Components -- Active Circuits -- Antennas -- System-on-Substrate (SoS) -- Fabrication Technologies and Materials -- Fabrication by PCB and LTCC Technologies -- Integration of SIW on Silicon -- Use of Novel Substrate Materials -- Solutio ns for High Frequency Operation of SIW
ISBN:9781608075355
Series:eBooks
Series:Artech eBooks
Keywords: Strip transmission lines. , Microwave transmission lines. , Microwave integrated circuits.
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Call number:9780750672917:ONLINE Show nearby items on shelf
Title:Reference data for engineers: radio, electronics, computer, and communications.
Author(s): M. E. Van Valkenburg (ed.)
Wendy Middleton (ed.)
Date:2002
Edition:9th ed.
Publisher:ScienceDirect
Size:1 online resource
Contents:Radio frequency spectrum management and time frequency standards -- International telephony recommendations -- Units, constants, and conversion factors -- Properties of materials -- Components or parts -- Fundamentals of networks -- Fourier waveform analysis -- Filters, simple bandpass design -- Filters, modern-network-theory design -- Active filter design -- Attenuators -- Measurements and analysis -- Magnetic-core transformers and reactors -- Power electronics -- rectifiers, filters, and power sup plies -- Feedback control systems -- Electron tubes -- Power grid-tube circuits -- Semiconductors and transistors -- Transistor circuits -- Integrated circuits -- Optoelectronics -- Optical communications -- Analog communications -- Digital communications -- Information theory and coding -- Computer communications networks -- Satellite and space communications -- Discrete-time signal processing -- Transmission lines -- Waveguides and resonators -- Scattering matrices -- Antennas -- Electromagnetic-wave pr opagation -- Radio noise and interference -- Broadcasting, cable television, and recording system standards -- Radar -- Radio navigation systems -- Common carrier transmission -- Switching networks and traffic concepts -- Electroacoustics -- Lasers -- Com puter organization and programming -- Logic design -- Probability and statistics -- Reliability and life testing -- Cellular telecommunications systems -- Mathematical equations -- Mathematical tables -- Miscellaneous data.
ISBN:9780750672917
Series:eBooks
Series:ScienceDirect
Keywords: Electronics. , Computer engineering. , Telecommunication.
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Call number:1786301091:ONLINE Show nearby items on shelf
Title:Fourier Analysis
Author(s): Ceschi
Date:2017
Publisher:Wiley-ISTE
Size:1 online resource (267 p.)
ISBN:9781786301093
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Electrical & Electronics Engineering
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Call number:0471889482:ONLINE Show nearby items on shelf
Title:Fourier Analysis of Time Series: An Introduction, Second Edition
Author(s): Bloomfield
Date:2000
Publisher:Wiley-Interscience
Size:1 online resource (289 p.)
ISBN:9780471889489
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Statistics
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Call number:0471694630:ONLINE Show nearby items on shelf
Title:Applications of Fourier Analysis on Finite Non-Abelian Groups in Signal Processing and System Design
Author(s): Stankovic
Date:2005
Publisher:Wiley-IEEE Press
Size:1 online resource (265 p.)
ISBN:9780471694632
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Electrical & Electronics Engineering
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Call number:0471669849:ONLINE Show nearby items on shelf
Title:Fourier Analysis
Author(s): Stade
Date:2005
Publisher:Wiley-Interscience
Size:1 online resource (521 p.)
ISBN:9780471669845
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Mathematics
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Call number:0470744812:ONLINE Show nearby items on shelf
Title:Fourier Analysis on Groups
Author(s): Rudin
Date:1962
Publisher:Wiley
Size:1 online resource (286 p.)
ISBN:9780470744819
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Mathematics
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Call number:0470294663:ONLINE Show nearby items on shelf
Title:Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing
Author(s): Broughton
Date:2008
Publisher:Wiley-Interscience
Size:1 online resource (361 p.)
ISBN:9780470294666
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Mathematics
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Call number:TK5102.5L298::2005 Show nearby items on shelf
Title:Linear Systems and Signals
Author(s): B. P. (Bhagwandas Pannalal) Lathi
Date:2005
Publisher:Oxford University Press
Note:2nd ed.
Contents:Signals and Systems
Time-Domain Analysis of Continuous-Time Systems
Time-Domain Analysis of Discrete-Time Systems
Continuous-Time System Analysis using the Laplace Transform
Discrete-Time System Analysis using the Z-Transform
Continuous-Time Signal Analysis : The Fourier Series
Continuous-Time Signal Analysis : The Fourier Transform
Sampling : The Bridge from Continuous to Discrete
Fourier Analysis of Discrete-Time Signals
State-Space Analysis
ISBN:0195158334
Keywords: Signal processing, Mathematics , System analysis , Linear time invariant systems , Digital filters (Mathematics)
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Call number:TK454.E46::2003 Show nearby items on shelf
Title:Schaum's outline of theory and problems of electric circuits
Author(s): Mahmood Nahvi
Joseph A. Edminister
Date:2003
Edition:4th ed.
Publisher:New York : McGraw-Hill
Size:469 p
Contents:Introduction -- Circuit concepts -- Circuit laws -- Analysis methods -- Amplifiers and operational circuits -- Waveforms and signals -- First order circuits -- Higher order circuits and complex frequency -- Sinusoidal steady state circuit analysis -- AC power -- Polyphase circuits -- Frequency response filters and resonance -- Two port networks -- Mutual inductance and transformers -- Circuit analysis using spice and pspice -- The laplace transform method -- fourier method of waveform analysis -- Complex number system -- Matrices an determinants
ISBN:9780071393072
Series:Schaum's outline series
Keywords: Electric circuits , Problems and exercises
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Call number:TA330.J44::2002 Show nearby items on shelf
Title:Advanced engineering mathematics
Author(s): Alan Jeffrey
Date:2002
Publisher:Harcourt Academic Press
Note:Volume 2 is the solutions manual
Contents:Review of Prerequisites
Vectors and Matrices
Vectors and Vector Spaces
Matrices and Systems of Linear Equations
Eigenvalues, Eigenvectors and Diagonalization
Ordinary Differential Equations
First Order Differential Equations
Second and Higher Order Linear Differential Equations and Systems
The Laplace Transform
Series Solutions of Differential Equations, Special Functions, and Sturm-Liouville Equations
Fourier Series
Fourier Integrals and the Fourier Transform
Vector Calculus
Vector Differential Calculus
Vector Integral Calculus
Complex analysis
Analytic Functions
Complex Integration
Laurent Series, Residues, and Contour Integration
The Laplace Inversion Integral
Particla Differential Equations
Numerical Mathematics
ISBN:012382592X
Keywords: Engineering mathematics
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Call number:SPRINGER-2016-9783662489932:ONLINE Show nearby items on shelf
Title:Mathematical Analysis II
Author(s): Vladimir A Zorich
Date:2016
Edition:2nd ed. 2016
Size:1 online resource (720 p.)
Note:10.1007/978-3-662-48993-2
Contents:9 Continuous Mappings (General Theory) -- 10 Differential Calculus from a General Viewpoint -- 11 Multiple Integrals -- 12 Surfaces and Differential Forms in Rn -- 13 Line and Surface Integrals -- 14 Elements of Vector Analysis and Field Theory -- 1 5 Integration of Differential Forms on Manifolds -- 16 Uniform Convergence and Basic Operations of Analysis -- 17 Integrals Depending on a Parameter -- 18 Fourier Series and the Fourier Transform -- 19 Asymptotic Expansions -- Topics and Questions for Mid term Examinations -- Examination Topics -- Examination Problems (Series and Integrals Depending on a Parameter) -- Intermediate Problems (Integral Calculus of Several Variables) -- Appendices: A Series as a Tool (Introductory Lecture) -- B Change of Varia bles in Multiple Integrals -- C Multidimensional Geometry and Functions of a Very Large Number of Variables -- D Operators of Field Theory in Curvilinear Coordinates -- E Modern Formula of Newton–Leibniz -- References -- Index of Basic
Notation -- Subject Index -- Name Index
ISBN:9783662489932
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Mathematical analysis , Analysis (Mathematics) , Physics , Mathematics , Analysis , Theoretical, Mathematical and Computational Physics
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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-2016-9783319311029:ONLINE Show nearby items on shelf
Title:Electrical Measurements in the Laboratory Practice
Author(s): Rosario Bartiromo
Date:2016
Size:1 online resource (286 p.)
Note:10.1007/978-3-319-31102-9
Contents:Electrical Circuits and components -- Direct current circuit analysis -- Uncertainty in electrical measurements -- Direct current measurements -- Alternating current circuit analysis -- Alternating current: special circuits --
Alternating current measurements -- The oscilloscope -- Circuit pulse response -- Transmission line -- App. A: Skin Effect -- App. B: Fourier Analysis
ISBN:9783319311029
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Physics , Electronic circuits , Physical measurements , Measurement , Electronics , Microelectronics , Physics , Measurement Science and Instrumentation , Electronics and Microelectronics, Instrumentation , Electronic Circuits and Devices
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Call number:SPRINGER-2016-9783319309675:ONLINE Show nearby items on shelf
Title:Writing Proofs in Analysis
Author(s): Jonathan M Kane
Date:2016
Size:1 online resource (4 p.)
Note:10.1007/978-3-319-30967-5
Contents:What Are Proofs, And Why Do We Write Them? -- The Basics of Proofs -- Limits -- Continuity -- Derivatives -- Riemann Integrals -- Infinite Series -- Sequences of Functions -- Topology of the Real Line -- Metric Spaces
ISBN:9783319309675
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Fourier analysis , Functional analysis , Mathematical logic , Mathematics , Functional Analysis , Fourier Analysis , Mathematical Logic and Foundations
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Call number:SPRINGER-2016-9783319290461:ONLINE Show nearby items on shelf
Title:Measure and Integration
Author(s): Hari Bercovici
Date:2016
Edition:1st ed. 2016
Size:1 online resource (300 p.)
Note:10.1007/978-3-319-29046-1
Contents:Rings of sets -- Measurability -- Integrals and Measures -- Convergence Theorems for Lebesgue Integrals -- Existence and Uniqueness of Measures -- Signed Measures, Complex Measures and Absolute Continuity -- Measure and Topology -- Product Measures -- The Lp Spaces -- Fourier Analysis -- Standard Measure Spaces.
ISBN:9783319290461
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Measure theory , Functions of real variables , Mathematics , Measure and Integration , Real Functions
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Call number:SPRINGER-2016-9783319287393:ONLINE Show nearby items on shelf
Title:Nonlocal Diffusion and Applications
Author(s): Claudia Bucur
Date:2016
Size:1 online resource (23 p.)
Note:10.1007/978-3-319-28739-3
Contents:Introduction -- 1 A probabilistic motivation.-1.1 The random walk with arbitrarily long jumps -- 1.2 A payoff model.-2 An introduction to the fractional Laplacian.-2.1 Preliminary notions -- 2.2 Fractional Sobolev Inequality and Generalized Coarea F ormula -- 2.3 Maximum Principle and Harnack Inequality -- 2.4 An s-harmonic function -- 2.5 All functions are locally s-harmonic up to a small error -- 2.6 A function with constant fractional Laplacian on the ball -- 3 Extension problems -- 3.1 Water wave model -- 3.2 Crystal dislocation -- 3.3 An approach to the extension problem via the Fourier transform -- 4 Nonlocal phase transitions -- 4.1 The fractional Allen-Cahn equation -- 4.2 A nonlocal version of a conjecture by De Giorgi -- 5 Nonlocal minimal surfaces -- 5.1 Graphs and s-minimal surfaces -- 5.2 Non-existence of singular cones in dimension 2 5.3 Boundary regularity -- 6 A nonlocal nonlinear stationary Schrödinger type equation -- 6.1 From the nonlocal Uncertainty Principle to a
fractional weighted inequality -- Alternative proofs of some results -- A.1 Another proof of Theorem A.2 Another proof of Lemma 2.3 -- References
ISBN:9783319287393
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes of the Unione Matematica Italiana: 20
Keywords: Mathematics , Functional analysis , Integral transforms , Operational calculus , Partial differential equations , Calculus of variations , Mathematics , Partial Differential Equations , Calculus of Variations and Optimal Control Optimization , Integral Transforms, Operational Calculus , Functional Analysis
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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-2016-9783319274669: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-2016-9783319272658:ONLINE Show nearby items on shelf
Title:Basic Concepts in Computational Physics
Author(s): Benjamin A Stickler
Date:2016
Edition:2nd ed. 2016
Size:1 online resource (409 p.)
Note:10.1007/978-3-319-27265-8
Contents:Some Basic Remarks -- Part I Deterministic Methods -- Numerical Differentiation -- Numerical Integration -- The KEPLER Problem -- Ordinary Differential Equations – Initial Value Problems -- The Double Pendulum -- Molecular Dynamics --
Numerics of Ordinary Differential Equations - Boundary Value Problems -- The One-Dimensional Stationary Heat Equation -- The One-Dimensional Stationary SCHRÖDINGER Equation -- Partial Differential Equations -- Part II Stochastic
Methods -- Pseudo Random Number Generators -- Random Sampling Methods -- A Brief Introduction to Monte-Carlo Methods -- The ISING Model -- Some Basics of Stochastic Processes -- The Random Walk and Diffusion Theory -- MARKOV-Chain
Monte Carlo and the POTTS Model -- Data Analysis -- Stochastic Optimization -- Appendix: The Two-Body Problem -- Solving Non-Linear Equations. The NEWTON Method -- Numerical Solution of Systems of Equations -- Fast Fourier Transform --
Basics of Probability Theory -- Phase Transitions -- Fractional Integrals and Derivatives in 1D -- Least Squares Fit -- Deterministic Optimization
ISBN:9783319272658
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Physics , Chemistry, Physical and theoretical , Computer mathematics , Applied mathematics , Engineering mathematics , Physics , Numerical and Computational Physics , Appl.Mathematics/Computational Methods of Engineering , Computational Mathematics and Numerical Analysis , Theoretical and Computational Chemistry
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Call number:SPRINGER-2016-9783034809641:ONLINE Show nearby items on shelf
Title:Application of Holomorphic Functions in Two and Higher Dimensions
Author(s): Klaus Gürlebeck
Date:2016
Size:1 online resource (3 p.)
Note:10.1007/978-3-0348-0964-1
Contents:1.Basic Properties of Holomorphic Functions -- 2.Conformal and Quasi-conformal Mappings -- 3.Function Theoretic Function spaces -- 4.Operator Calculus -- 5.Decompositions -- 6.Some First Order Systems of Partial Differential Equations -- 7.Boundary Value Problems of Second Order Partial Differential Equations -- 8.Some Initial-boundary Value Problems -- 9.Riemann-Hilbert Problems -- 10.Initial Boundary Value Problems on the Sphere -- 11.Fourier Transforms -- Bibliography -- Index
ISBN:9783034809641
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Functional analysis , Functions of complex variables , Integral transforms , Operational calculus , Partial differential equations , Mathematics , Integral Transforms, Operational Calculus , Functions of a Complex Variable , Partial Differential Equations , Functional Analysis
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Call number:SPRINGER-2014-9783642540752:ONLINE Show nearby items on shelf
Title:Upper and Lower Bounds for Stochastic Processes [electronic resource] : Modern Methods and Classical Problems
Author(s): Michel Talagrand
Date:2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:The book develops modern methods and in particular the generic chaining to bound stochastic processes. This methods allows in particular to get optimal bounds for Gaussian and Bernoulli processes. Applications are given tostable processes, infinitely divisible processes, matching theorems, the convergence of random Fourier series, of orthogonal series, and to functional analysis. The complete solution of a number of classical problems is given incomplete detail, and an ambitious program for future re search is laid out
Contents:0. Introduction
1. Philosophy and Overview of the Book
2. Gaussian Processes and the Generic Chaining
3. Random Fourier Series and Trigonometric Sums, I
4. Matching Theorems I
5. Bernouilli Processes
6. Trees and the Art of Lower Bounds
7. Random Fourier Series and Trigonometric Sums, II
8. Processes Related to Gaussian Processes
9. Theory and Practice of Empirical Processes
10. Partition Scheme for Families of Distances
11. Infinitely Divisible Processes
12. The Fundamental Conjectures
13. Convergence of Orthogonal Series Majorizing Measures
14. Matc
ISBN:9783642540752
Series:eBooks
Series:SpringerLink
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 0071-1136 : v60
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Distribution (Probability theory)
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Call number:SPRINGER-2014-9783642538599:ONLINE Show nearby items on shelf
Title:Laser Spectroscopy 1 [electronic resource] : Basic Principles
Author(s): Wolfgang Demtrder
Date:2014
Edition:5th Edition
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Keeping abreast of the latest techniques and applications, this new edition of the standard reference and graduate text on laser spectroscopy has been completely revised and expanded. While the general concept is unchanged, thenew edition features a broad array of new material, e.g., ultrafast lasers (atto- and femto-second lasers) and parametric oscillators, coherent matter waves, Doppler-free Fourier spectroscopy with optical frequency combs, interferencespectroscopy, quantum optics, the interferom etric detection of gravitational waves and still more applications in chemical analysis, medical diagnostics, and engineering
Contents:Introduction
Absorption and Emission of Light
Widths and Profiles of Spectral Lines
Spectroscopic Instrumentation
Lasers as Spectroscopic Sources
Solutions
ISBN:9783642538599
Series:eBooks
Series:SpringerLink
Series:Physics and Astronomy (Springer-11651)
Keywords: Spectroscopy , Microwaves , Surfaces (Physics)
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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-2014-9783319064475:ONLINE Show nearby items on shelf
Title:Regularity of Difference Equations on Banach Spaces [electronic resource]
Author(s): Ravi P Agarwal
Claudio Cuevas
Carlos Lizama
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevantresults. They address recent advances in the field, as well as basic semigroup and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research.This book is intended for graduate students and res earchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis
Contents:1.Discrete Semi groups and Cosine Operators
2. Maximal regularity and the method of Fourier Multipliers
3. First Order Linear Difference Equations
4. First Order Semi linear Difference Equations
5. Second Order Linear Difference Equations
6. Second Order Semi linear
7. Applications
ISBN:9783319064475
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional equations
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Call number:SPRINGER-2014-9783319060743:ONLINE Show nearby items on shelf
Title:Functional Analysis and Applied Optimization in Banach Spaces [electronic resource] : Applications to Non-Convex Variational Models
Author(s): Fabio Botelho
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physicsand engineering probl ems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation.Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dualapproach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in relatedfields
Contents:1. Topological Vector Spaces
2. The Hahn
Bananch Theorems and Weak Topologies
3. Topics on Linear Operators
4.Basic Results on Measure and Integration
5. The Lebesgue Measure in Rn
6. Other Topics in Measure and Integration
7. Distributions
8. The Lebesque and Sobolev Spaces
9. Basic Concepts on the Calculus of Variations
10. Basic Concepts on Convex Analysis
11. Constrained Variational Analysis
12. Duality Applied to Elasticity
13. Duality Applied to a Plate Model
14. About Ginzburg
Landau Type Equations: The Simpler Real Case
15. Full Complex Ginzb
ISBN:9783319060743
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Functional analysis , Numerical analysis
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Call number:SPRINGER-2014-9783319045375:ONLINE Show nearby items on shelf
Title:Sparse Grids and Applications - Munich 2012 [electronic resource]
Author(s): Jochen Garcke
Dirk Pflger
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Sparse grids have gained increasing interest in recent years for the numerical treatment of high-dimensional problems. Whereas classical numerical discretization schemes fail in more than three or four dimensions, sparse gridsmake it possible to over come the curse of dimensionality to some degree, extending the number of dimensions that can be dealt with. This volume of LNCSE collects the papers from the proceedings of the second workshop on sparsegrids and applications, demonstrating once again the importance of this numerical discretization scheme. The selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures, andthe range of applications extends to uncertainty quantification settings a nd clustering, to name but a few examples
Contents:Gerrit Buse, Dirk Pfluger, and Riko Jacob: Efficient Pseudorecursive Evaluation Schemes for Non
Adaptive Sparse Grids
Oliver G. Ernst and Bjorn Sprungk: Stochastic Collocation for Elliptic PDEs with Random Data The Lognormal Case
Michael Griebel and Helmut Harbrecht: On the Convergence of the Combination Technique
Michael Griebel and Jan Hamaekers: Fast Discrete Fourier Transform on Generalized Sparse Grids
Michael Griebel and Jens Oettershagen: Dimension
adaptive Sparse Grid Quadrature for Integrals with Boundary Singularities
Max Gunzburger, Clayton G. Webster, and Gua
ISBN:9783319045375
Series:eBooks
Series:SpringerLink
Series:Lecture Notes in Computational Science and Engineering, 1439-7358 : v97
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science Mathematics , Computer science
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Call number:SPRINGER-2014-9783319026428:ONLINE Show nearby items on shelf
Title:Multiple Wiener-It Integrals [electronic resource] : With Applications to Limit Theorems
Author(s): Pter Major
Date:2014
Edition:2nd ed. 2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The goal of this Lecture Note is to prove a new type of limit theorems for normalized sums of strongly dependent random variables that play an important role in probability theory or in statistical physics. Here non-linearfunctionals of stationary Ga ussian fields are considered, and it is shown that the theory of WienerIt integrals provides a valuable tool in their study. More precisely, a version of these random integrals is introduced thatenables us to combine the technique of random integrals and Fourier analysis. The most important results of this theory are presented together with some non-trivial limit theorems proved with their help. This work is a new, revisedversion of a previous volume written with the goalof giving a better explanation of some of the details and the motivation behind the proofs. It does not contain essentially new results it was written to give a better insight to theold ones. In particular, a more detailed explanation of generalized fields is included to show that what is at the first sight a rather formal object is actually a useful tool for carryingout heuristic arguments
ISBN:9783319026428
Series:eBooks
Series:SpringerLink
Series:Lecture Notes in Mathematics, 0075-8434 : v849
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Distribution (Probability theory)
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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-2014-9783319022918:ONLINE Show nearby items on shelf
Title:Discrete Dynamical Models [electronic resource]
Author(s): Ernesto Salinelli
Franco Tomarelli
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several disciplineas Mathematical Analysi s, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems arepresented, paying particular attention to the stabil ity analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to thestudy of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. Thebook is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Eco nomics. The exposition is self-contained: some appendices present prerequisites, algorithms and suggestions for computer simulations.The analysis of several examples is enriched by the proposition of many related exercises of increasing difficulty in the last chapter the detailed solution is given for most of them
Contents:1 Recursive phenomena and difference equations
2 Linear difference equations
3 Discrete dynamical systems: one
step scalar equations
4 Complex behavior of nonlinear dynamical systems: bifurcations and chaos
5 Discrete dynamical systems: vector equations
6 Markov chains
7 Matrix
8 Solutions
ISBN:9783319022918
Series:eBooks
Series:SpringerLink
Series:UNITEXT, 2038-5714 : v76
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Functional equations , Differentiable dynamical systems
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Call number:SPRINGER-2014-9783319020990:ONLINE Show nearby items on shelf
Title:Introduction to Partial Differential Equations [electronic resource]
Author(s): Peter J Olver
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, andelsewhere. The exposition car efully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, andinclude straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material thatmotivates the student to delve further into the subject. No previous experien ce with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- andmulti-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to formthe core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximu m Principle, financial models, dispersion and solitons, Huygens' Principle, quantum mechanical systems,and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes ar e an important component of any introductory course, and the text covers the twomost basic approaches: finite differences and finite elements. Peter J. Olver is professor of mathematics at the University of Minnesota. His wide-ranging research interests a re centered on the development of symmetry-based methodsfor differential equations and their manifold applications. He is the author of over 130 papers published in major scientific research
Contents:What are Partial Differential Equations?
Linear and Nonlinear Waves
Fourier Series
Separation of Variables
Finite Differences
Generalized Functions and Greens Functions
Complex Analysis and Conformal Mapping
Fourier Transforms
Linear and Nonlinear Evolution Equations
A General Framework forLinear Partial Differential Equations
FiniteElements and Weak Solutions
Dynamics of Planar Media
Partial Differential Equations in Space .
ISBN:9783319020990
Series:eBooks
Series:SpringerLink
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Differential equations, partial
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Call number:SPRINGER-2014-9781461488279:ONLINE Show nearby items on shelf
Title:A Qualitative Approach to Inverse Scattering Theory [electronic resource]
Author(s): Fioralba Cakoni
David Colton
Date:2014
Publisher:Boston, MA : Springer US : Imprint: Springer
Size:1 online resource
Note:Inverse scattering theory is an important area of applied mathematics due to its central role in such areas as medical imaging , nondestructive testing and geophysical exploration. Until recently all existing algorithms forsolving inverse scattering problems were based on using either a weak scattering assumption or on the use of nonlinear optimization techniques. The limitations of these methods have led in recent years to an alternative approach to theinverse scattering problem which avoids the inc orrect model assumptions inherent in the use of weak scattering approximations as well as the strong a priori information needed in order to implement nonlinear optimization techniques.These new methods come under the general title of qualitative methods in inverse scattering theory and seek to determine an approximation to the shape of the scattering object as well as estimates on its material properties withoutmaking any weak scattering assumption and using essentially no a priori information on the nat ure of the scattering object. This book is designed to be an introduction to this new approach in inverse scattering theory focusing on theuse of sampling methods and transmission eigenvalues. In order to aid the reader coming from a discipline outside of mathematics we have included background material on functional analysis, Sobolev spaces, the theory of ill posedproblems and certain topics in in the theory of entire functions of a complex variable. This book is an updated and expanded version of an ear lier book by the authors published by Springer titled Qualitative Methods in InverseScattering Theory Review of Qualitative Methods in Inverse Scattering Theory All in all, the authors do exceptionally well in combining such a wide variety of mathematical material and in presenting it in a well-organized andeasy-to-follow fashion. This text certainly complements the growing body of work in inverse scattering and should well suit both new researchers to
Contents:1. Functional Analysis and Sobolev Spaces
2. Ill
Posed Problems
3. Scattering by Imperfect Conductors
4. Inverse Scattering Problems for Imperfect Conductors
5. Scattering by Orthotropic Media
6. Inverse Scattering Problems for Orthotropic Media
7. Factorization Methods
8. Mixed Boundary Value Problems
9. Inverse Spectral Problems for Transmission Eigenvalues
10. A Glimpse at Maxwell's Equations
ISBN:9781461488279
Series:eBooks
Series:SpringerLink
Series:Applied Mathematical Sciences, 0066-5452 : v188
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Differential equations, partial , Computer engineering
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Call number:SPRINGER-2014-9781461458111:ONLINE Show nearby items on shelf
Title:Symmetric Discontinuous Galerkin Methods for 1-D Waves [electronic resource] : Fourier Analysis, Propagation, Observability and Applications
Author(s): Aurora Marica
Enrique Zuazua
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform meshes.First,a careful Fourier analysis is constructed, highlightingthe coexistence of two Fourier spectral branches or spectral diagrams (physical and spurious) related to the two components of the numerical solution (averages andjumps). Efficient filtering mechanisms are also develo pedby means of techniques previously proved to be appropriate for classical schemes like finite differences or P1-classical finite elements. In particular,the work presents aproof thatthe uniform observability property is recovered uniformly by considerin g initial data with null jumps and averages given by a bi-grid filtering algorithm. Finally, the bookexplains how theseresults can be extended toother more sophisticated conforming and non-conforming finite element methods, in particular to quadratic fini teelements, local discontinuous Galerkin methods and a version of the SIPG method adding penalization on the normalderivatives of the numerical solution at the grid points. This work is the first publication tocontaina rigorous analysis of the discontinuo us Galerkin methods for wave control problems. It will be of interest to a range ofresearchers specializing inwave approximations
Contents:1. Preliminaries
2. Discontinuous Galerkin approximations and main results
3. Bibliographical notes
4. Fourier analysis of the DG methods
5. Nonuniform observability for DG approximations of waves
6. Filtering mechanisms
7. Extensions to other numerical approximation schemes
8. Comments and open problems
A technical proof
References
ISBN:9781461458111
Series:eBooks
Series:SpringerLink
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Differential equations, partial , Algorithms , Numerical analysis
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Call number:SPRINGER-2014-9781447164340:ONLINE Show nearby items on shelf
Title:Mathematical Methods for Elastic Plates [electronic resource]
Author(s): Christian Constanda
Date:2014
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Mathematical models of deformation of elastic plates are used by applied mathematicians and engineers in connection with a wide range of practical applications, from microchip production to the construction of skyscrapers andaircraft. This book emplo ys two important analytic techniques to solve the fundamental boundary value problems for the theory of plates with transverse shear deformation, which offers a more complete picture of the physical process ofbending than Kirchhoffs classical one. The fi rst method transfers the ellipticity of the governing system to the boundary, leading to singular integral equations on the contour of the domain. These equations, established on thebasis of the properties of suitable layer potentials, are then solved in spaces of smooth (Hlder continuous and Hlder continuously differentiable) functions. The second technique rewrites the differential system in terms ofcomplex variables and fully integrates it, expressing the solution as a combination of complex analytic potentials. The last chapter develops a generalized Fourier series method closely connected with the structure of the system,which can be used to compute approximate solutions. The numerical results generated as an illustration for the interior Dirichlet problem are accompanied by remarks regarding the efficiency and accuracy of the procedure. Thepresentation of the material is detailed and self-contained, making Mathematical Methods for Elastic Plates accessible to researchers and graduate students wit h a basic knowledge of advanced calculus
Contents:Singular Kernels
Potentials and Boundary Integral Equations
Bending of Elastic Plates
The Layer Potentials
The Newtonian Potential
Existence of Regular Solutions
Complex Variable Treatment
Generalized Fourier Series
ISBN:9781447164340
Series:eBooks
Series:SpringerLink
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Integral equations , Materials
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Call number:SPRINGER-2014-9781447163954:ONLINE Show nearby items on shelf
Title:An Introduction to Laplace Transforms and Fourier Series [electronic resource]
Author(s): Phil Dyke
Date:2014
Edition:2nd ed. 2014
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative.Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis onapplication with the necessary mathematical g rounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Onlyknowledge of elementary trigonometry and calculus are required as prereq uisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics ormathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and biological modelling requiring techniques for solving initial value problems
Contents:The Laplace Transform
Further Properties of the Laplace Transform
Convolution and the Solution of Ordinary Differential Equations
Fourier Series
Partial Differential Equations
Fourier Transforms
Wavelets and Signal Processing
Complex Variables and Laplace Transforms
ISBN:9781447163954
Series:eBooks
Series:SpringerLink
Series:Springer Undergraduate Mathematics Series, 1615-2085
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Functions of complex variables , Integral Transforms , Mathematical physics , Engineering mathematics
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Call number:SPRINGER-2013-9789462390096:ONLINE Show nearby items on shelf
Title:Applied Mathematics [electronic resource] : Data Compression, Spectral Methods, Fourier Analysis, Wavelets, and Applications
Author(s): Charles K Chui
Qingtang Jiang
Date:2013
Publisher:Paris : Atlantis Press : Imprint: Atlantis Press
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This textbook, apart from introducing the basic aspects of applied mathematics, focuses on recent topics such as information data manipulation, information coding, data approximation, data dimensionality reduction, datacompression, time-frequency and time scale bases, image manipulation, and image noise removal. The methods treated in more detail include spectral representation and frequency of the data, providing valuable information for, e.g.data compression and noise removal. Furthermore, a specia l emphasis is also put on the concept of wavelets in connection with the multi-scale structure of data-sets. The presentation of the book is elementary and easilyaccessible, requiring only some knowledge of elementary linear algebra and calculus. All impo rtant concepts are illustrated with examples, and each section contains between 10 an 25 exercises. A teaching guide, depending on the leveland discipline of instructions is included for classroom teaching and self-study
Note:Springer eBooks
Contents:Linear Spaces
Linerar Analysis
Spectral Methods and Applications
Frequency
Domain Methods
Data Compression
Fourier Series
Fourier Time
Frequency Methods
Wavelet Transform and Filter Banks
Compactly Supported Wavelets
Wavelet Analysis
ISBN:9789462390096
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics Textbooks for Science and Engineering : v2
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer vision , Statistics , Engineering design
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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-2013-9783319011950:ONLINE Show nearby items on shelf
Title:Mathematical Physics [electronic resource] : A Modern Introduction to Its Foundations
Author(s): Sadri Hassani
Date:2013
Edition:2nd ed. 2013
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics asdiverse as algebras, cla ssical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups,manifolds, Lie groups and their representations , Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of thefirst one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition,namely the balance between rigor and physical application, has been maintained, as is the abun dance of historical notes and worked out examples that demonstrate the unreasonable effectiveness of mathematics in modern physics.Einstein has famously said, The most incomprehensible thing about nature is that it is comprehensible. What he had in mind w as reiterated in another one of his famous quotes concerning the question of how ... mathematics, beingafter all a product of human thought, is so admirably appropriate to the objects of reality. It is a question that comes to everyone's mind when encoun tering the highly abstract mathematics required for a deep understanding of modernphysics. It is the experience that Eugene Wigner so profoundly described as the unreasonable effectiveness of mathematics in the natural sciences.
Note:Springer eBooks
Contents:Mathematical Preliminaries
I Finite
Dimensional Vector Spaces
1 Vectors and Linear Maps
2 Algebras
3 Operator Algebra
4 Matrices
5 Spectral Decomposition
II Infinite
Dimensional Vector Spaces
6 Hilbert Spaces
7 Classical Orthogonal Polynomials
8 Fourier Analysis
III Complex Analysis
9 Complex Calculus
10 Calculus of Residues
11 Advanced Topics
IV Differential Equations
12 Separation of Variables in Spherical Coordinates
13 Second
Order Linear Differential Equations
14 Complex Analysis of SOLDEs
15 Integral Transforms and Differential Equ
ISBN:9783319011950
Series:e-books
Series:SpringerLink (Online service)
Series:Physics and Astronomy (Springer-11651)
Keywords: Mathematics , Mathematical physics
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Call number:SPRINGER-2013-9783319004013:ONLINE Show nearby items on shelf
Title:Computational Physics [electronic resource] : Simulation of Classical and Quantum Systems
Author(s): Philipp O.J Scherer
Date:2013
Edition:2nd ed. 2013
Publisher:Heidelberg : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics.Many clear mathemati cal descriptions of important techniques in computational physics are given. The first part of the book discusses the basic numerical methods. A large number of exercises and computer experiments allows to study theproperties of these methods. The second part concentrates on simulation of classical and quantum systems. It uses a rather general concept for the equation of motion which can be applied to ordinary and partial differential equations.Several classes of integration methods are discussed includin g not only the standard Euler and Runge Kutta method but also multistep methods and the class of Verlet methods which is introduced by studying the motion in Liouville space.Besides the classical methods, inverse interpolation is discussed, together with the popular combined methods by Dekker and Brent and a not so well known improvement by Chandrupatla. A general chapter on the numerical treatment ofdifferential equations provides methods of finite differences, finite volumes, finite elements and boundar y elements together with spectral methods and weighted residual based methods. A comparison of several methods for quantumsystems is performed, containing pseudo-spectral methods, finite differences methods, rational approximation to the time evolution op erator, second order differencing and split operator methods. The book gives simple but non trivialexamples from a broad range of physical topics trying to give the reader insight into the numerical treatment but also the simulated problems. Rotational mo tion is treated in much detail to describe the motion of rigid rotors which canbe just a simple spinning top or a collection of molecules or planets. The behaviour of simple quantum systems is studied t
Note:Springer eBooks
Contents:Part I Numerical Methods
Error Analysis
Interpolation
Numerical Differentiation
Numerical Integration
Systems of Inhomogeneous Linear Equations
Roots and Extremal Points
Fourier Transformation
Random Numbers and Monte
Carlo Methods
Eigenvalue Problems
Data Fitting
Discretization of Differential Equations
Equations of Motion
Part II Simulation of Classical and Quantum Systems
Rotational Motion
Molecular Dynamics
Thermodynamic Systems
Random Walk and Brownian Motion
Electrostatics
Waves
Diffusion
Nonlinear Systems
Simple Quantum S
ISBN:9783319004013
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Physics, 1868-4513
Series:Physics and Astronomy (Springer-11651)
Keywords: Chemistry , Engineering mathematics
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Call number:SPRINGER-2013-9783034806039:ONLINE Show nearby items on shelf
Title:Quaternion and Clifford Fourier Transforms and Wavelets [electronic resource]
Author(s): Eckhard Hitzer
Stephen J Sangwine
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Quaternion andClifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering.This edited volume pres ents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamiltons quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all itssubspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts. This book provides comprehensiveinsights into current developments and applications including their performa nce and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms forhypercomplex algebras, which will help readers to see that software implementations are within our gra sp. It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms andwavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the con tributions that follow relate to each other and to prior work. The book will be a valuable resource forgraduate students as well as for scientists and engineers
Note:Springer eBooks
Contents:Preface
History of Quaternion and Clifford
Fourier Transforms and Wavelets
Part I: Quaternions
1 Quaternion Fourier Transform: Re
tooling Image and Signal Processing Analysis
2 The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations
3 Quaternionic Spectral Analysis of Non
Stationary Improper Complex Signals
4 Quaternionic Local Phase for Low
level Image Processing Using Atomic Functions
5 Bochners Theorems in the Framework of Quaternion Analysis
6 Bochner
Minlos Theorem and Quaternion Fourier Transform
Part II: Clifford Algeb
ISBN:9783034806039
Series:e-books
Series:SpringerLink (Online service)
Series:Trends in Mathematics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer vision , Matrix theory , Fourier analysis , Numerical analysis , Number theory
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Call number:SPRINGER-2013-9783034802949:ONLINE Show nearby items on shelf
Title:The Weyl Operator and its Generalization [electronic resource]
Author(s): Leon Cohen
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 deals with the theory and application of associating a function of two variables with a function of two operators that do not commute. The concept of associating ordinary functions with operators has arisen in many areasof science and mathe matics, and up to the beginning of the twentieth century many isolated results were obtained. These developments were mostly based on associating a function of one variable with one operator, the operator generallybeing the differentiation operator. With the discovery of quantum mechanics in the years 1925-1930, there arose, in a natural way, the issue that one has to associate a function of two variables with a function of two operators that donot commute. Methods to do so became known as rules of associ ation, correspondence rules, or ordering rules. This has led to a wonderfully rich mathematical development that has found applications in many fields. Subsequently it wasrealized that for every correspondence rule there is a corresponding phase-space dis tribution. Now the fields of correspondence rules and phase-space distributions are intimately connected. A similar development occurred in the fieldof time-frequency analysis where the aim is to understand signals with changing frequencies. The Weyl Oper ator and Its Generalization aims at bringing together the basic results of the field in a unified manner. A wide audience isaddressed, particularly students and researchers who want to obtain an up-to-date working knowledge of the field. The mathematics i s accessible to the uninitiated reader and is presented in a straightforward manner
Note:Springer eBooks
Contents:Introduction
The Fundamental Idea, Terminology, and Operator Algebra
The Weyl Operator
The Algebra of the Weyl Operator
Product of Operators, Commutators, and the Moyal Sin Bracket
Some Other Ordering Rules
Generalized Operator Association
The Fourier, Monomial, and Delta Function Associations
Transformation Between Associations
Path Integral Approach
The Distribution of a Symbol and Operator
The Uncertainty Principle
Phase
Space Distributions
Amplitude, Phase, Instantaneous Frequency, and the Hilbert Transform
Time
Frequency Analysis
The Transfor
ISBN:9783034802949
Series:e-books
Series:SpringerLink (Online service)
Series:Pseudo-Differential Operators, Theory and Applications : v9
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Operator theory , Differential equations, partial
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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
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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-2013-9781461482598:ONLINE Show nearby items on shelf
Title:Prolate Spheroidal Wave Functions of Order Zero [electronic resource] : Mathematical Tools for Bandlimited Approximation
Author(s): Andrei Osipov
Vladimir Rokhlin
Hong Xiao
Date:2013
Publisher:Boston, MA : Springer US : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Prolate Spheroidal Wave Functions (PSWFs) are the eigenfunctions of the bandlimited operator in one dimension. As such, they play an important role in signal processing, Fourier analysis, and approximation theory. Whilehistorically the numerical eval uation of PSWFs presented serious difficulties, the developments of the last fifteen years or so made them as computationally tractable as any other class of special functions. As a result, PSWFs havebeen becoming a popular computational tool. The present book serves as a complete, self-contained resource for both theory and computation. It will be of interest to a wide range of scientists and engineers, from mathematiciansinterested in PSWF as an analytical tool to electrical engineers designing filters and antennas
Note:Springer eBooks
Contents:Introduction
Mathematical and Numerical Preliminaries
Overview
Analysis of the Differential Operator
Analysis of the Integral Operator
Rational Approximations of PSWFs
Miscellaneous Properties of PSWFs
Asymptotic Analysis of PSWFs
Quadrature Rules and Interpolation via PSWFs
Numerical Algorithms
ISBN:9781461482598
Series:e-books
Series:SpringerLink (Online service)
Series:Applied Mathematical Sciences, 0066-5452 : v187
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Numerical analysis , Engineering mathematics
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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-2013-9781461467861:ONLINE Show nearby items on shelf
Title:Principles of Musical Acoustics [electronic resource]
Author(s): William M Hartmann
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:Principles of Musical Acoustics focuses on the basic principles in the science and technology of music. Musical examples and specific musical instruments demonstrate the principles. The book begins with a study of vibrations andwaves, in that order. These topics constitute the basic physical properties of sound, one of two pillars supporting the science of musical acoustics. The second pillar is the human element, the physiological and psychological aspectsof acoustical science. The perceptual topics include loudness, pitch, tone color, and localization of sound. With these two pillars in place, it is possible to go in a variety of directions. The book treats in turn, the topics of roomacoustics, audio both analog and digital, broadcasting, and speec h. It ends with chapters on the traditional musical instruments, organized by family. The mathematical level of this book assumes that the reader is familiar withelementary algebra. Trigonometric functions, logarithms and powers also appear in the book, b ut computational techniques are included as these concepts are introduced, and there is further technical help in appendices
Note:Springer eBooks
Contents:Sound, Music, and Science
Vibrations 1
Vibrations 2
Instrumentation
Sound Waves
Wave Properties
Standing Waves
Standing Waves in Pipes
Fourier Analysis and Synthesis
Sound Intensity
The Auditory System
Loudness Perception
Pitch
Localization of Sound
Sound Environments
Audio Transducers
Distortion and Noise
Audio Systems
Loudspeakers
Digital Audio
Broadcasting
Speech
Brass Musical Instruments
Woodwind Instruments
String Instruments
Percussion Instruments
Electronic Music
ISBN:9781461467861
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Lecture Notes in Physics, 2192-4791
Series:Physics and Astronomy (Springer-11651)
Keywords: Neurobiology , Acoustics , Acoustics in engineering
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Call number:SPRINGER-2013-9781461466604:ONLINE Show nearby items on shelf
Title:Approximation Theory and Harmonic Analysis on Spheres and Balls [electronic resource]
Author(s): Feng Dai
Yuan Xu
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 monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book containsmainstream material on the s ubject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part ofthe book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate studentsin analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewiczmultiplier theorem, the Riesz transform, and doubling weights are all familiar tools to re searchers in this area
Note:Springer eBooks
Contents:1 Spherical Harmonics
2 Convolution and Spherical Harmonic Expansion
3 Littlewood
Paley Theory and Multiplier Theorem
4 Approximation on the Sphere
5 Weighted Polynomial Inequalities
6 Cubature Formulas on Spheres
7 Harmonic Analysis Associated to Reflection Groups
8 Boundedness of Projection Operator and Cesro Means
9 Projection Operators and Cesro Means in L^p Spaces
10 Weighted Best Approximation by Polynomials
11 Harmonic Analysis on the Unit Ball
12 Polynomial Approximation on the Unit Ball
13 Harmonic Analysis on the Simplex
14 Applications
ISBN:9781461466604
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Fourier analysis , Functions, special
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Call number:SPRINGER-2013-9781461460060:ONLINE Show nearby items on shelf
Title:Wavelets Made Easy [electronic resource]
Author(s): Yves Nievergelt
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:Originally published in 1999, Wavelets Made Easyoffers a lucid and concise explanation of mathematical wavelets.Written at the level of a first course in calculus and linear algebra, its accessible presentation is designedfor undergraduates in a vari ety of disciplinescomputer science, engineering, mathematics, mathematical sciencesas well as for practicing professionals in these areas. The presentsoftcover reprintretainsthecorrectionsfromthesecond printing (2001) andmakesthis uniquetext available to a wider audience. The first chapter startswith a description of the key features and applications of wavelets, focusing on Haar's wavelets but using onlyhigh-school mathematics. The next two chapters introduce one-, two-, and three-dimensional wavelets, with only the occasional use of matrix algebra. The second part of this book provides the foundations of least-squaresapproximation, the discrete Fourier transform, and Fourier series. The third part explains the Fourier transform and then demonstrates h ow to apply basic Fourier analysis to designing and analyzing mathematical wavelets. Particularattention is paid to Daubechies wavelets. Numerous exercises, a bibliography, and a comprehensive index combine to make this book an excellent text for the cla ssroom as well as a valuable resource for self-study
Note:Springer eBooks
Contents:Preface
Outline
A. Algorithms for Wavelet Transforms
Haar's Simple Wavelets
Multidimensional Wavelets and Applications
Algorithms for Daubechies Wavelets
B. Basic Fourier Analysis
Inner Products and Orthogonal Projections
Discrete and Fast Fourier Transforms
Fourier Series for Periodic Functions
C. Computation and Design of Wavelets
Fourier Transforms on the Line and in Space
Daubechies Wavelets Design
Signal Representations with Wavelets. D. Directories
Acknowledgements
Collection of Symbols
Bibliography
Index.
ISBN:9781461460060
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Harmonic analysis , Fourier analysis , Computer science Mathematics , Computer engineering
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