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SPIRES-BOOKS: FIND KEYWORD REAL FUNCTIONS *END*INIT* use /tmp/qspiwww.webspi1/19091.59 QRY 131.225.70.96 . find keyword real functions ( in books using www Cover
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Call number:SPRINGER-2016-9789811009723:ONLINE Show nearby items on shelf
Title:Linear Functional Analysis for Scientists and Engineers
Author(s): Balmohan V Limaye
Date:2016
Size:1 online resource (254 p.)
Note:10.1007/978-981-10-0972-3
Contents:Chapter 1. Preliminaries -- Chapter 2. Basic Framework -- Chapter 3. Bounded Linear Maps -- Chapter 4. Dual Spaces, Transposes and Adjoints -- Chapter 5. Spectral Theory
ISBN:9789811009723
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Functional analysis , Functions of real variables , Mathematics , Functional Analysis , Real Functions
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Call number:SPRINGER-2016-9783319323770:ONLINE Show nearby items on shelf
Title:Pi: The Next Generation A Sourcebook on the Recent History of Pi and Its Computation
Author(s): David H Bailey
Date:2016
Size:1 online resource (507 p.)
Note:10.1007/978-3-319-32377-0
Contents:Foreword -- Preface -- Introduction -- Computation of pi using arithmetic-geometric mean -- Fast multiple-precision evaluation of elementary functions -- The arithmetic-geometric mean of Gauss -- The arithmetic-geometric mean and fast computation of elementary functions -- A simplified version of the fast algorithms of Brent and Salamin -- Is pi normal? -- The computation of pi to 29,360,000 decimal digits using Borweins' quartically convergent algorithm -- Gauss, Landen, Ramanujan, the arithmetic-g eometric mean, ellipses, pi, and the ladies diary -- Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of pi calculation.-Ramanujan and pi -- 11. Ramanujan, modular equations, and approximations to pi or how to compute one billion digits of pi -- Pi, Euler numbers, and asymptotic expansions -- A spigot algorithm for the digits of pi -- On the rapid computation of various polylogarithmic constants -- Similarities in irrationality proofs for pi, ln 2, ζ(2),
and ζ(3) -- Unbounded spigot algorithms for the digits of pi -- Mathematics by experiment: Plausible reasoning in the 21st century -- Approximations to pi derived from integrals with nonnegative integrands -- Ramanujan's series for 1/π: A survey - - The computation of previously inaccessible digits of π2 and Catalan's constant -- Walking on real numbers -- Birth, growth and computation of pi to ten trillion digits -- Pi day is upon us again and we still do not know if pi is normal -- The Life of p i -- I prefer pi: A brief mathematical history and anthology of articles in the American Mathematical Monthly -- Bibliography -- Index
ISBN:9783319323770
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Computer mathematics , History , Number theory , Mathematics , Computational Mathematics and Numerical Analysis , Number Theory , History of Mathematical Sciences
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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-2016-9783319307442:ONLINE Show nearby items on shelf
Title:Real Analysis
Author(s): Peter A Loeb
Date:2016
Size:1 online resource (274 p.)
Note:10.1007/978-3-319-30744-2
Contents:Preface -- Set Theory and Numbers -- Measure on the Real Line -- Measurable Functions -- Integration -- Differentiation and Integration -- General Measure Spaces -- Introduction to Metric and Normed Spaces -- Hilbert Spaces -- Topological Spaces -- Measure Construction -- Banach Spaces -- Appendices -- References.
ISBN:9783319307442
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Functional analysis , Measure theory , Functions of real variables , Mathematics , Real Functions , Functional Analysis , Measure and Integration
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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-2016-9783319290256:ONLINE Show nearby items on shelf
Title:Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control
Author(s): Russell Johnson
Date:2016
Edition:1st ed. 2016
Size:1 online resource (497 p.)
Note:10.1007/978-3-319-29025-6
Contents:Nonautonomous linear Hamiltonian systems -- The rotation number and the Lyapunov index for real nonautonomous linear Hamiltonian systems -- The Floquet coeffcient for nonautonomous linear Hamiltonian systems: Atkinson problems -- The Weyl functions -- Weak disconjugacy for linear Hamiltonian systems -- Nonautonomous control theory. Linear regulator problem and the Kalman-Bucy filter -- Nonautonomous control theory. A general version of the Yakubovich Frequency Theorem -- Nonautonomous control theor y. Linear-quadratic dissipative control processes -- Index -- References
ISBN:9783319290256
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Developments in Mathematics: 36
Keywords: Mathematics , Dynamics , Ergodic theory , Differential equations , System theory , Mathematics , Dynamical Systems and Ergodic Theory , Ordinary Differential Equations , Systems Theory, Control
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Call number:SPRINGER-2016-9783319284002:ONLINE Show nearby items on shelf
Title:Introduction to Calculus and Classical Analysis
Author(s): Omar Hijab
Date:2016
Edition:4th ed. 2016
Size:1 online resource (1 p.)
Note:10.1007/978-3-319-28400-2
Contents:Preface -- A Note to the Reader -- 1. The Set of Real Numbers -- 2. Continuity -- 3. Differentiation.-4. Integration -- 5. Applications -- 6. Generalizations -- A. Solutions -- References -- Index
ISBN:9783319284002
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Approximation theory , Sequences (Mathematics) , Special functions , Combinatorics , Mathematics , Approximations and Expansions , Sequences, Series, Summability , Special Functions , Combinatorics
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Call number:SPRINGER-2016-9783319281063:ONLINE Show nearby items on shelf
Title:University of Toronto Mathematics Competition (2001–2015)
Author(s): Edward J Barbeau
Date:2016
Size:1 online resource (1 p.)
Note:10.1007/978-3-319-28106-3
Contents:Preface -- 1. Problems of the Contests -- 2. Algebra -- 3. Inequalities -- 4. Sequences and Series -- 5. Calculus and its Applications -- 6. Other Topics in Analysis -- 7. Linear Algebra -- 8. Geometry -- 9. Group Theory -- 10. Combinatorics and Fi nite Mathematics -- 11. Number Theory -- Appendix A: Definitions, Conventions, Notation, and Basics -- Appendix B: Top-Ranking Students -- Index.
ISBN:9783319281063
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Group theory , Differential equations , Functions of real variables , Geometry , Mathematics , Real Functions , Geometry , Group Theory and Generalizations , Ordinary Differential Equations
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Call number:SPRINGER-2016-9783319279565:ONLINE Show nearby items on shelf
Title:Several Real Variables
Author(s): Shmuel Kantorovitz
Date:2016
Edition:1st ed. 2016
Size:1 online resource (307 p.)
Note:10.1007/978-3-319-27956-5
Contents:Continuity -- Derivation -- Implicit Functions -- Integration -- Solutions.
ISBN:9783319279565
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Functions of real variables , Mathematics , Real Functions
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Call number:SPRINGER-2016-9783319278070:ONLINE Show nearby items on shelf
Title:Advanced Calculus of a Single Variable
Author(s): Tunc Geveci
Date:2016
Size:1 online resource (77 p.)
Note:10.1007/978-3-319-27807-0
Contents:Preface -- Real Numbers, Sequences and Limits -- Limits and Continuity of Functions -- The Derivative -- The Riemann Integral -- Infinite Series -- Sequences and Series of Functions. Index.
ISBN:9783319278070
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Functional analysis , Integral transforms , Operational calculus , Mathematics , Integral Transforms, Operational Calculus , Functional Analysis
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Call number:SPRINGER-2016-9783319273235:ONLINE Show nearby items on shelf
Title:Non-Archimedean Operator Theory
Author(s): Toka Diagana
Date:2016
Size:1 online resource (156 p.)
Note:10.1007/978-3-319-27323-5
ISBN:9783319273235
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Field theory (Physics) , Functional analysis , Operator theory , Functions of real variables , Mathematics , Operator Theory , Functional Analysis , Field Theory and Polynomials , Real Functions
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Call number:SPRINGER-2014-9784431549192:ONLINE Show nearby items on shelf
Title:Bernoulli Numbers and Zeta Functions [electronic resource]
Author(s): Tsuneo Arakawa
Tomoyoshi Ibukiyama
Masanobu Kaneko
Date:2014
Publisher:Tokyo : Springer Japan : Imprint: Springer
Size:1 online resource
Note:Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powersof consecutive integers . The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advancedtopics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers a formula for Bernoulli numbers by Stirling numbers the Clausenvon Staudttheorem on the denominators of Bernoulli numbers Kummer's congruence betw een Bernoulli numbers and a related theory of p-adic measures the EulerMaclaurin summation formula the functional equation of the Riemann zeta function andthe Dirichlet L functions, and their special values at suitable integers various formulas of exponen tial sums expressed by generalized Bernoulli numbers the relation between ideal classes of orders of quadratic fields and equivalenceclasses of binary quadratic forms class number formula for positive definite binary quadratic forms congruences between so me class numbers and Bernoulli numbers simple zeta functions of prehomogeneous vector spaces Hurwitz numbers
ISBN:9784431549192
Series:eBooks
Series:SpringerLink
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Global analysis (Mathematics) , Number theory
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Call number:SPRINGER-2014-9783319062099:ONLINE Show nearby items on shelf
Title:From Real to Complex Analysis [electronic resource]
Author(s): R. H Dyer
D. E Edmunds
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis andtopology. Beginning with the theory of the Riemann integral (and its improper extension) on the real line, the fundamentals of metric spaces are then developed, with special attention being paid to connectedness, simple connectednessand various forms of homotopy. The final chapter d evelops the theory of complex analysis, in which emphasis is placed on the argument, the winding number, and a general (homology) version of Cauchy's theorem which is proved using theapproach due to Dixon. Special features are the inclusion of proofs of M ontel's theorem, the Riemann mapping theorem and the Jordan curve theorem that arise naturally from the earlier development. Extensive exercises are included ineach of the chapters, detailed solutions of the majority of which are given at the end. From Re al to Complex Analysis is aimed at senior undergraduates and beginning graduate students in mathematics. It offers a sound grounding inanalysis in particular, it gives a solid base in complex analysis from which progress to more advanced topics may be mad e
Contents:The Riemann integral
Metric spaces
Complex Analysis
Sets and functions
ISBN:9783319062099
Series:eBooks
Series:SpringerLink
Series:Springer Undergraduate Mathematics Series, 1615-2085
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables
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Call number:SPRINGER-2014-9783319052243:ONLINE Show nearby items on shelf
Title:Descriptive Topology and Functional Analysis [electronic resource] : In Honour of Jerzy Kakols 60th Birthday
Author(s): Juan Carlos Ferrando
Manuel Lpez-Pellicer
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Descriptive topology and functional analysis, with extensive material demonstrating new connections between them, are the subject of the first section of this work. Applications to spaces of continuous functions, topologicalAbelian groups, linear top ological equivalence and to the separable quotient problem are included and are presented as open problems. The second section is devoted to Banach spaces, Banach algebras and operator theory. Each chapterpresents a lot of worthwhile and important recent theorems with an abstract discussing the material in the chapter. Each chapter can almost be seen as a survey covering a particular area
Contents:1Some aspects in the Mathematical work of Jerzy Kakol
2Weak barrelledness vs. P
spaces
3On the topology of the sets of the real projections of the zeros ofexponential polynomials
4The density character of the space Cp(X)
5Compactness and distances to spaces of continuous functions andFrchet spaces
6Two classes of metrizable spaces lc
invariant
7Characteristics of the Mackey topology for abelian topologicalgroups
8Bowens Entropy for Endomorphisms of Totally Bounded Abelian
9On preserved and unpreserved extreme pointsGroups
10Cantor set
ISBN:9783319052243
Series:eBooks
Series:SpringerLink
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v80
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Functional analysis , Operator theory , Topology
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Call number:SPRINGER-2014-9783319041476:ONLINE Show nearby items on shelf
Title:Networks and Network Analysis for Defence and Security [electronic resource]
Author(s): Anthony J Masys
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Networks and Network Analysis for Defence and Security discusses relevant theoretical frameworks and applications of network analysis in support of the defence and security domains. This book details real world applications ofnetwork analysis to supp ort defence and security. Shocks to regional, national and global systems stemming from natural hazards, acts of armed violence, terrorism and serious and organized crime have significant defence and securityimplications. Today, nations face an uncertain and complex security landscape in which threats impact/target the physical, social, economic and cyber domains. Threats to national security, such as that against critical infrastructuresnot only stem from man-made acts but also from natural hazards. Katr ina (2005), Fukushima (2011) and Hurricane Sandy (2012) are examples highlighting the vulnerability of critical infrastructures to natural hazards and the cripplingeffect they have on the social and economic well-being of a community and a nation. With th is dynamic and complex threat landscape, network analysis has emerged as a key enabler in supporting defence and security. With the advent ofbig data and increasing processing power, network analysis can reveal insights with regards to structural and dyna mic properties thereby facilitating greater understanding of complex networks, their entities, interdependencies,vulnerabilities to produce insights for creative solutions. This book will be well positioned to inform defence, security and intelligence pro fessionals and researchers with regards to leading methodologies and approaches
Contents:Network Analysis in Criminal Intelligence
Identifying mafia Bosses from Meeting Attendance
Macrosocial Network Analysis: the Case of Transnational Drug Trafficking
Policing the Hackers by Hacking them: Studying Online Deviants in IRC Chat Rooms
Why Terror Networks are Dissimilar: How Structure Relates to Functions
Social Network Analysis Applied to Criminal Networks: Recent Developments in Dutch Law Enforcement
The Networked Mind
Collective Identities and the Cognitive
Affective Nature of Conflict
Conflict Cessation and the Emergence of Weapons Supermarkets
A Conspirac
ISBN:9783319041476
Series:eBooks
Series:SpringerLink
Series:Lecture Notes in Social Networks, 2190-5428
Series:Physics and Astronomy (Springer-11651)
Keywords: Social sciences Data processing , Mathematics , Criminology
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Call number:SPRINGER-2014-9783319038476:ONLINE Show nearby items on shelf
Title:Computations with Modular Forms [electronic resource] : Proceedings of a Summer School and Conference, Heidelberg, August/September 2011
Author(s): Gebhard Bckle
Gabor Wiese
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg. A key theme of theConference and Summer School was the interplay between theory, algorithms and experiment. The 14 papers offer readers both, instructional courses on the latest algorithms for computing modular and automorphic forms, as well as originalresearch articles reporting on the latest develop ments in the field. The three Summer School lectures provide an introduction to modern algorithms together with some theoretical background for computations of and with modular forms,including computing cohomology of arithmetic groups, algebraic automorph ic forms, and overconvergent modular symbols. The 11 Conference papers cover a wide range of themes related to computations with modular forms, including latticemethods for algebraic modular forms on classical groups, a generalization of the Maeda conject ure, an efficient algorithm for special values of p-adic Rankin triple product L-functions, arithmetic aspects and experimental data ofBianchi groups, a theoretical study of the real Jacobian of modular curves, results on computing weight one modular form s, and more
Contents:Part I Summer School: Lectures on Computing Cohomology of Arithmetic Groups by P.E. Gunnells
Computing with Algebraic Automorphic Forms by D. Loeffler
Overconvergent Modular Symbols by R. Pollack
Part II Conference and Research Contributions: Congruence Subgroups, Cusps and Manin Symbols over Number Fields by J. E. Cremona and M. T. Arans
Computing Weight One Modular Forms over C and Fp by K. Buzzard
Lattice Methods for Algebraic Modular Forms on Classical Groups by M. Greenberg and J. Voight
Efficient Computation of Rankin p
Adic L
Functions by A.G.B. Lauder
Formes Modu
ISBN:9783319038476
Series:eBooks
Series:SpringerLink
Series:Contributions in Mathematical and Computational Sciences, 2191-303X : v6
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic , Algorithms , Number theory
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Call number:SPRINGER-2014-9783319027654:ONLINE Show nearby items on shelf
Title:Convergence Estimates in Approximation Theory [electronic resource]
Author(s): Vijay Gupta
Ravi P Agarwal
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The study of linear positive operators is an area of mathematical studies with significant relevance to studies of computer-aided geometric design, numerical analysis, and differential equations. This book focuses on theconvergence of linear positive operators in real and complex domains. The theoretical aspects of these operators have been an active area of research over the past few decades. In this volume, authors Gupta and Agarwal explore new andmore efficient methods of applying this research to studies in Optimization and Analysis. The text will be of interest to upper-level students seeking an introduction to the field and to researchers developing innovative approaches
Contents:1.Preliminaries
2. Approximation by Certain Operators
3. Complete Asymptotic Expansion
4. Linear and Iterative Combinations
5. Better Approximation
6. Complex Operators in Compact Disks
7. Rate of Convergence for Functions of BV
8. Convergence for BV/Bounded Functions on Bezier Variants
9. Some More Results on Rate of Convergence
10. Rate of Convergence in Simultaneous Approximation
11. Future Scope and Open Problems
ISBN:9783319027654
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Operator theory , Differential equations, partial
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Call number:SPRINGER-2014-9783319023687:ONLINE Show nearby items on shelf
Title:A Course in Point Set Topology [electronic resource]
Author(s): John B Conway
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs.Prerequisites include calculus and at least one semester ofanalysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other topological notions in the real line.Appendices areincluded to bridge the gap between this new material and material found in an analysis course. Metric spaces are one of the more prevalent topological spaces used in other areas and are therefore introduced in the first chapter andemphasized throughout the text. This also conforms to the approach of the book to start with the particular and work toward the more general. Chapter 2 defines and develops abstract topological spaces, with metric spaces as the sourceof inspiration, and with a focus on Hausdorff spaces.The final chapter concentrates on continuous real -valued functions, culminating in a development of paracompact spaces
Contents:Metric Spaces
Topological Spaces
Continuous Real
Valued Functions
Appendix
Bibliography
Terms
Symbols
ISBN:9783319023687
Series:eBooks
Series:SpringerLink
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topology
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Call number:SPRINGER-2014-9783319020693:ONLINE Show nearby items on shelf
Title:Inspired by Finance [electronic resource] : The Musiela Festschrift
Author(s): Yuri Kabanov
Marek Rutkowski
Thaleia Zariphopoulou
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The present volume is dedicated to Marek Musiela, the eminent scholar and practitioner, well-known for his important contribution into problems of derivative pricing, theory of term structure of interest rates, theory ofdefaultable securities and oth er topics of modern mathematical finance. Under the cover the reader finds 25 research papers of 47 authors, famous or young, covering the whole range of the hot topics of the discipline. Thecontributed articles not only give a clear picture about what is going on in this fast developing field of knowledge but provide methods ready for practical implementation. They also open perspectives for further studies in riskmanagement, portfolio optimization, and financial engineering
Contents:R. Ahlip and M. Rutkowski: Forward Start Foreign Exchange Options under Hestons Volatility and the CIR Interest R
A. Bensoussan and S. R. Hoe:Real Options with Competition and Incomplete Market
T. R. Bielecki and S. Crpey: Dynamic Hedging of Counterparty Exposure
L. Campi:A Note on Market Completeness with American Put Options
S. Cawston and L. Vostrikova: An f
Divergence Approach for Optimal Portfolios in Exponential Lvy Models
B. Chouaf and S. Pergamenchtchikov: Optimal Investment with Bounded VaR for Power Utility Functions
T. Choulli, J. Ma and M
A. Morlais:Three
ISBN:9783319020693
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Finance
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Call number:SPRINGER-2014-9783319017211:ONLINE Show nearby items on shelf
Title:Modal Interval Analysis [electronic resource] : New Tools for Numerical Information
Author(s): Miguel A Sainz
Joaquim Armengol
Remei Calm
Pau Herrero
Lambert Jorba
Josep Vehi
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This book presents an innovative new approach to interval analysis. Modal Interval Analysis (MIA) is an attempt to go beyond the limitations of classic intervals in terms of their structural, algebraic and logical features. Thestarting point of MIA i s quite simple: It consists in defining a modal interval that attaches a quantifier to a classical interval and in introducing the basic relation of inclusion between modal intervalsby means ofthe inclusionof the sets of predicates they accept. This modal approach introduces interval extensions of the real continuous functions, identifies equivalences between logical formulas and interval inclusions, and provides the semantic theoremsthat justify these equivalences, along with guidelines for arriving at t hese inclusions. Applications of these equivalences in different areas illustrate the obtained results. The book also presents a new interval object: marks, whichaspire to be a new form of numerical treatment of errors in measurements and computations
Contents:Intervals
Modal Intervals
Modal interval extensions
Interpretability and optimality
Interval arithmetic
Equations and systems
Twins and f
star algorithm
Marks
Intervals of marks
Some related problems
ISBN:9783319017211
Series:eBooks
Series:SpringerLink
Series:Lecture Notes in Mathematics, 0075-8434 : v2091
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Electronic data processing , Global analysis (Mathematics)
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Call number:SPRINGER-2014-9783034806220:ONLINE Show nearby items on shelf
Title:Real Quaternionic Calculus Handbook [electronic resource]
Author(s): Joo Pedro Morais
Svetlin Georgiev
Wolfgang Sprig
Date:2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Real quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativity, electrodynamics, spin etc., it has developed into a body of material that interacts with many branches of mathematics, suchas complex analysis, harmonic analysis, differential geometry, and differential equations. It is also a ubiquitous factor in the description and elucidation of problems in mathematical physics. In the meantime real quaternion analysishas become a well established branch in ma thematics and has been greatly successful in many different directions. This book is based onconcrete examples and exercises rather than general theorems, thus making it suitable for anintroductory one- or two-semester undergraduate course on some of the major aspects of real quaternion analysis in exercises. Alternatively, it may be used for beginning graduate level courses and as a reference work. With exercises atthe end of each chapter and its straightforward writing style the book addresses readers w ho have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as real and complex analysis,ordinary differential equations, partial differential equations, and theory of distributions
Contents:1 An introduction to quaternions
2 Quaternions and spatial rotation
3 Quaternion sequences
4 Quaternion series and infinite products
5 Exponents and logarithms
6 Trigonometric functions
7 Hyperbolic functions
8 Inverse hyperbolic and trigonometric functions
9 Quaternion matrices
10 Monomials, polynomials and binomials
11 Solutions
Bibliography
Index
ISBN:9783034806220
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Algebra , Functions of complex variables , Combinatorics , Geometry
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Call number:SPRINGER-2014-9781461496380:ONLINE Show nearby items on shelf
Title:Real Analysis for the Undergraduate [electronic resource] : With an Invitation to Functional Analysis
Author(s): Matthew A Pons
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis.While these advanced t opics are not typically encountered until graduate study, the text is designed for the beginner. The authors engaging style makes advanced topics approachable without sacrificing rigor. The text alsoconsistently encourages the reader to pick up a pencil a nd take an active part in the learning process. Key features include: - examples to reinforce theory - thorough explanations preceding definitions, theorems and formal proofs -illustrations to support intuition - over 450 exercises designed to develop con nections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delvedeeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate cu rriculum
Contents:The Real Numbers
Sequences in R
Numerical Series
Continuity
The Derivative
Sequence and Series of Functions
The Riemann Integral
Lebesgue Measure on R
Lebesgue Integration
ISBN:9781461496380
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functional analysis
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Call number:SPRINGER-2014-9781461488545:ONLINE Show nearby items on shelf
Title:Set Theory [electronic resource] : With an Introduction to Real Point Sets
Author(s): Abhijit Dasgupta
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbookpresents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins withthe DedekindPeano axioms and ends with the construction of the real numbers. The core CantorDedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundationalissues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theorysuch as the resolution of Lusin's problems on projective sets using determinacy of infinite ga mes and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable forstudents interested in any field of mathematics, not just for those planning to specialize in logic or foundations. The re is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semesteror one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a r elevant or adjacent area and beginners wanting to learn set theory via self-study
Contents:1 Preliminaries: Sets, Relations, and Functions
Part I Dedekind: Numbers
2 The DedekindPeano Axioms
3 Dedekinds Theory of the Continuum
4 Postscript I: What Exactly Are the Natural Numbers?
Part II Cantor: Cardinals, Order, and Ordinals
5 Cardinals: Finite, Countable, and Uncountable
6 Cardinal Arithmetic and the Cantor Set
7 Orders and Order Types
8 Dense and Complete Orders
9 Well
Orders and Ordinals
10 Alephs, Cofinality, and the Axiom of Choice
11 Posets, Zorns Lemma, Ranks, and Trees
12 Postscript II: Innitary Combinatorics
Part III Re
ISBN:9781461488545
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic , Algebra , Global analysis (Mathematics) , Logic, Symbolic and mathematical , Topology
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Call number:SPRINGER-2014-9781461471325:ONLINE Show nearby items on shelf
Title:Walter Gautschi, Volume 3 [electronic resource] : Selected Works with Commentaries
Author(s): Claude Brezinski
Ahmed Sameh
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He isworld renowned for his pi oneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi:Selected Works with Commentaries, is a compilation of G autschis most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemoratingWalters prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical ConditioningSpecial Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other QuadraturesGauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and B iography Miscellanea Works of Werner Gautschi
Contents:Part I Commentaries
Linear recurrence relations
Ordinary differential equations
Computer algorithms and software packages
History and biography
Miscellanea
Part II Reprints
Linear difference equations
Ordinary differential equations
Computer algorithms and software packages
History and biography
Miscellanea
Part III Werner Gautschi
Publications
Obituaries
Recording
ISBN:9781461471325
Series:eBooks
Series:SpringerLink
Series:Contemporary Mathematicians
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Differential Equations , Numerical analysis
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Call number:SPRINGER-2014-9781461470496:ONLINE Show nearby items on shelf
Title:Walter Gautschi, Volume 2 [electronic resource] : Selected Works with Commentaries
Author(s): Claude Brezinski
Ahmed Sameh
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He isworld renowned for his pi oneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi:Selected Works with Commentaries, is a compilation of G autschis most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemoratingWalters prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical ConditioningSpecial Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other QuadraturesGauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and B iography Miscellanea Works of Werner Gautschi
Contents:Part I Commentaries
Orthogonal polynomials on the real line
Polynomials orthogonal on the semicircle
Chebyshev quadrature
Kronrod and other quadratures
Gauss type quadrature
Part II Reprints
Orthogonal polynomials on the real line
Polynomials orthogonal on the semicircle
Chebyshev quadrature
Kronrod and other quadratures
ISBN:9781461470496
Series:eBooks
Series:SpringerLink
Series:Contemporary Mathematicians
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Differential Equations , Numerical analysis
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Call number:SPRINGER-2014-9781461470342:ONLINE Show nearby items on shelf
Title:Walter Gautschi, Volume 1 [electronic resource] : Selected Works with Commentaries
Author(s): Claude Brezinski
Ahmed Sameh
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He isworld renowned for his pi oneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi:Selected Works with Commentaries, is a compilation of G autschis most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemoratingWalters prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical ConditioningSpecial Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other QuadraturesGauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and B iography Miscellanea Works of Werner Gautschi
Contents:Preface
Part I Walter Gautschi
Biography of Walter Gautschi
A brief summary of my scientific work and highlights of my career
Publications
Part II Commentaries
Numerical conditioning
Special functions
Interpolation and approximation
Part III Reprints
Numerical conditioning
Special functions
Interpolation and approximation
ISBN:9781461470342
Series:eBooks
Series:SpringerLink
Series:Contemporary Mathematicians
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Differential Equations , Numerical analysis
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Call number:SPRINGER-2014-9781447164227:ONLINE Show nearby items on shelf
Title:Potential Theory [electronic resource]
Author(s): Lester L Helms
Date:2014
Edition:2nd ed. 2014
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Potential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible. The subject matter is developed fromfirst principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem, the author develops methods for constructing solutions of Laplace's equation on aregion with prescribed values on the boundary of the region. The latter half of the book addresses more advanced material aimed at those with the background of a senior undergraduate or beginning graduate course in real analysis.Starting with solutions of the Dirichlet problem subject to mixed bounda ry conditions on the simplest of regions, methods of morphing such solutions onto solutions of Poisson's equation on more general regions are developed usingdiffeomorphisms and the Perron-Wiener-Brelot method, culminating in application to Brownian motion . In this new edition, many exercises have been added to reconnect the subject matter to the physical sciences. This book willundoubtedly be useful to graduate students and researchers in mathematics, physics, and engineering
Contents:Preliminaries
Laplaces Equation
The Dirichlet Problem
Green Functions
Negligible Sets
Dirichlet Problem for Unbounded Regions
Energy
Interpolation and Monotonicity
Newtonian Potential
Elliptic Operators
Apriori Bounds
Oblique Derivative Problem
Application to Diffusion Processes
ISBN:9781447164227
Series:eBooks
Series:SpringerLink
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial , Potential theory (Mathematics) , Distribution (Probability theory)
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Call number:SPRINGER-2013-9789491216862:ONLINE Show nearby items on shelf
Title:Single Variable Differential and Integral Calculus [electronic resource] : Mathematical Analysis
Author(s): Elimhan Mahmudov
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:The book Single variable Differential and Integral Calculus is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book isunique in the field of mathemat ical analysis in content and in style. It aims to define, compare and discuss topics in single variable differential and integral calculus, as well as giving application examples in important businessfields. Some elementary concepts such as the power of a set, cardinality, measure theory, measurable functions are introduced. It also covers real and complex numbers, vector spaces, topological properties of sets, series and sequencesof functions (including complex-valued functions and functions of a complex variable), polynomials and interpolation and extrema of functions. Although analysis is based on the single variable models and applications, theorems andexamples are all set to be converted to multi variable extensions. For example, Newton, Riemann, Sti eltjes and Lebesque integrals are studied together and compared
Note:Springer eBooks
Contents:Introduction to Numbers and Set Theory
Sequences and Series
Limits and Continuity of Functions
Differential Calculus
Some Basic Properties of Differentiable Functions
Polynomials and Interpolations
Applications of Differential Calculus to Limit Calculations and Extremum Problems
The Indefinite Integral
The Definite Integral
Applications of the Definite Integral
ISBN:9789491216862
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Differential Equations
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Call number:SPRINGER-2013-9783642321993:ONLINE Show nearby items on shelf
Title:Noncommutative Iwasawa Main Conjectures over Totally Real Fields [electronic resource] : Mnster, April 2011
Author(s): John Coates
Peter Schneider
R Sujatha
Otmar Venjakob
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives.Non-commutative Iwas awa theory has emerged dramatically over the last decade, culminating in the recent proof of the non-commutative main conjecture for the Tate motive over a totally real p-adic Lie extension of a number field,independently by Ritter and Weiss on the one ha nd, and Kakde on the other. The initial ideas for giving a precise formulation of the non-commutative main conjecture were discovered by Venjakob, and were then systematically developedin the subsequent papers by Coates-Fukaya-Kato-Sujatha-Venjakob and Fu kaya-Kato. There was also parallel related work in this direction by Burns and Flach on the equivariant Tamagawa number conjecture. Subsequently, Kato discovered animportant idea for studying the K_1 groups of non-abelian Iwasawa algebras in terms of the K_1 groups of the abelian quotients of these Iwasawa algebras. Kakde's proof is a beautiful development of these ideas of Kato, combined with anidea of Burns, and essentially reduces the study of the non-abelian main conjectures to abelian ones. The appro ach of Ritter and Weiss is more classical, and partly inspired by techniques of Frohlich and Taylor. Since many of the ideasin this book should eventually be applicable to other motives, one of its major aims is to provide a self-contained exposition of s ome of the main general themes underlying these developments. The present volume will be a valuableresource for researchers working in both Iwasawa theory and the theory of automorphic forms.
Note:Springer eBooks
Contents:Preface
John Coates, Dohyeong Kim: Introduction to the work of M. Kakde on the non
commutative main conjectures for totally real fields
R. Sujatha: Reductions of the main conjecture
Ted Chinburg, Georgios Pappas, Martin J. Taylor: The group logarithm past and present
Peter Schneider, Otmar Venjakob: K_1 of certain Iwasawa algebras, after Kakde
Mahesh Kakde: Congruences between abelian p
adic zeta functions
Otmar Venjakob: On the work of Ritter and Weiss in comparison with Kakde's approach
Malte Witte: Noncommutative Main Conjectures of Geometric Iwasawa Theory
ISBN:9783642321993
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v29
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , K-theory , Number theory
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Call number:SPRINGER-2013-9783319015774:ONLINE Show nearby items on shelf
Title:The Real Numbers [electronic resource] An Introduction to Set Theory and Analysis
Author(s): John Stillwell
Date:2013
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbersto model the line, an d to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theoryuncountability, the axiom of choice, and large cardinals. In fact, virtually all theconcepts of infinite set theory are needed fo r a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines adown-to-earth introduction to set theory with an exposition of the essen ce of analysisthe study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate studentsand professional mathematicians who, until now, have been content to assume the real numbers. I ts prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of realnumber and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich pr esentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will helpmotivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncoun table sets, countable ordinals, the continuum problem, the CantorSchrderBernsteintheorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions
Note:Springer eBooks
Contents:The Fundamental Questions
From Discrete to Continuous
Infinite Sets
Functions and Limits
Open Sets and Continuity
Ordinals
The Axiom of Choice
Borel Sets
Measure Theory
Reflections
Bibliography
Index
ISBN:9783319015774
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical
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Call number:SPRINGER-2013-9783319012407:ONLINE Show nearby items on shelf
Title:Structure of Approximate Solutions of Optimal Control Problems [electronic resource]
Author(s): Alexander J Zaslavski
Date:2013
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This titleexamines the structure of approximate solutions of optimal control problems considered on subintervals of a real line. Specifically at the properties of approximate solutions which are independent of the length of theinterval. The results i llustrated in this book look into the so-called turnpike property of optimal control problems. The author generalizes theresultsof the turnpike property by considering a class of optimal control problemswhich is identified with the corresponding complete metric space of objective functions.This establishes the turnpike property for any element in a set that is ina countable intersectionwhich is open everywhere dense sets in thespace of integrands meaning that the turnpike property holds for most optimal c ontrol problems. Mathematicians working in optimal control and the calculus of variations and graduate students will find this bookuseful and valuabledue to its presentation of solutions to a number of difficult problems in optimal controland presentation of new approaches, techniques and methods
Note:Springer eBooks
Contents:Preface
1.Introduction
2.Turnpike Properties of Optimal Control Problems
3.Infinite Horizon Problems
4.Linear Control Systems
References.
ISBN:9783319012407
Series:e-books
Series:SpringerLink (Online service)
Series:SpringerBriefs in Optimization, 2190-8354
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Systems theory , Mathematical optimization
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Call number:SPRINGER-2013-9783319008493:ONLINE Show nearby items on shelf
Title:Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces [electronic resource]
Author(s): Toka Diagana
Date:2013
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as wellas their recent gene ralizations. Some of the results presented are either new or else cannot be easily found in the mathematical literature. Despite the noticeable and rapid progress made on these important topics, the only standardreferences that currently exist on those ne w classes of functions and their applications are still scattered research articles. One of the main objectives of this book is to close that gap. The prerequisites for the book is the basicintroductory course in real analysis. Depending on the background of the student, the book may be suitable for a beginning graduate and/or advanced undergraduate student. Moreover, it will be of a great interest to researchers inmathematics as well as in engineering, in physics, and related areas. Further, some parts o f the book may be used for various graduate and undergraduate courses
Note:Springer eBooks
Contents:1. Metric, Banach, and Hilbert Spaces
2. Linear Operators on Banach Spaces
3. Almost Periodic Functions
4. Almost Automorphic Functions
5. Pseudo
Almost Periodic Functions
6. Pseudo
Almost Automorphic Functions
7. Existence Results for Some Second
Order Differential Equations
8. Existence Results to Some Integrodifferential Equations
9. Existence of C(m)
Pseudo
Almost Automorphic Solutions
10. Pseudo
Almost Periodic Solutions to Some Third
Order Differential Equations
11. Pseudo
Almost Automorphic Solutions to Some Sobolev
Type Equations
12. Stability Results f
ISBN:9783319008493
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Harmonic analysis , Operator theory , Differential Equations , Differential equations, partial
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Call number:SPRINGER-2013-9783034804783:ONLINE Show nearby items on shelf
Title:Functional Analysis in Asymmetric Normed Spaces [electronic resource]
Author(s): tefan Cobza
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:An asymmetric norm is a positive definite sublinear functional p on a real vector space X. The topology generated by the asymmetric norm p is translation invariant so that the addition is continuous, but the asymmetry of the normimplies that the mult iplication by scalars is continuous only when restricted to non-negative entries in the first argument. The asymmetric dual of X, meaning the set of all real-valued upper semi-continuous linear functionals on X, ismerely a convex cone in the vector space of all linear functionals on X. In spite of these differences, many results from classical functional analysis have their counterparts in the asymmetric case, by taking care of the interplaybetween the asymmetric norm p and its conjugate. Among the positi ve results one can mention: HahnBanach type theorems and separation results for convex sets, KreinMilman type theorems, analogs of the fundamental principles open mapping, closed graph and uniform boundedness theorems an analog of the Schauders theorem o n the compactness of the conjugate mapping. Applications are given to best approximation problems and, as relevant examples, oneconsiders normed lattices equipped with asymmetric norms and spaces of semi-Lipschitz functions on quasi-metric spaces. Since t he basic topological tools come from quasi-metric spaces and quasi-uniform spaces, the first chapter of thebook contains a detailed presentation of some basic results from the theory of these spaces. The focus is on results which are most used in function al analysis completeness, compactness and Baire category which drasticallydiffer from those in metric or uniform spaces. The book is fairly self-contained, the prerequisites being the acquaintance with the basic results in topology and functional analys is, so it may be used for an introduction to thesubject.Since new results, in the focus of current research, are also included, researchers in the area can use it as a reference
Note:Springer eBooks
Contents:Introduction
1. Quasi
metric and Quasi
uniform Spaces. 1.1. Topological properties of quasi
metric and quasi
uniform spaces
1.2. Completeness and compactness in quasi
metric and quasi
uniform spaces
2. Asymmetric Functional Analysis
2.1. Continuous linear operators between asymmetric normed spaces
2.2. Hahn
Banach type theorems and the separation of convex sets
2.3. The fundamental principles
2.4. Weak topologies
2.5. Applications to best approximation
2.6. Spaces of semi
Lipschitz functions
Bibliography
Index
ISBN:9783034804783
Series:e-books
Series:SpringerLink (Online service)
Series:Frontiers in Mathematics, 1660-8046
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Operator theory , Topology
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Call number:SPRINGER-2013-9783034804691:ONLINE Show nearby items on shelf
Title:Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals [electronic resource]
Author(s): Sergey Kislyakov
Natan Kruglyak
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
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Note:In this book we suggest a unified method of constructing near-minimizers for certain important functionals arising in approximation, harmonic analysis and ill-posed problems and most widely used in interpolation theory. Theconstructions are based on far-reaching refinements of the classical CaldernZygmund decomposition. These new CaldernZygmund decompositions in turn are produced with the help of new covering theorems that combine manyremarkable features of classical resultsestablished byBesicovitch, Whitney and Wiener. In many cases the minimizers constructed in the book are stable (i.e., remain near-minimizers) under the action of CaldernZygmund singularintegral operators. The book is divided into two parts. While the new method is presented in gre at detail in the second part, the first is mainly devoted to the prerequisites needed for a self-contained presentation of the main topic.There we discuss the classical covering results mentioned above, various spectacular applications of the classical Ca ldernZygmund decompositions, and the relationship of all this to real interpolation. It also serves as a quickintroduction to such important topics as spaces of smooth functions or singular integrals
Note:Springer eBooks
Contents:Preface
Introduction
Definitions, notation, and some standard facts
Part 1. Background
Chapter 1. Classical CaldernZygmund decomposition and real interpolation
Chapter 2. Singular integrals
Chapter 3. Classical covering theorems
Chapter 4. Spaces of smooth functions and operators on them
Chapter 5. Some topics in interpolation
Chapter 6. Regularization for Banach spaces
Chapter 7. Stability for analytic Hardy spaces
Part 2. Advanced theory
Chapter 8. Controlled coverings
Chapter 9. Construction of near
minimizers
Chapter 10. Stability of near
mini
ISBN:9783034804691
Series:e-books
Series:SpringerLink (Online service)
Series:Monografie Matematyczne : v74
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis
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Call number:SPRINGER-2013-9781461481546:ONLINE Show nearby items on shelf
Title:Elliptically Contoured Models in Statistics and Portfolio Theory [electronic resource]
Author(s): Arjun K Gupta
Tamas Varga
Taras Bodnar
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:Elliptically Contoured Models in Statistics and Portfolio Theory fully revises the first detailed introduction to the theory of matrix variate elliptically contoured distributions. There are two additional chapters, and all theoriginal chapters of th is classic text have been updated. Resources in this book will be valuable for researchers, practitioners, and graduate students in statistics and related fields of finance and engineering. Those interested inmultivariate statistical analysis and its appl ication to portfolio theory will find this text immediately useful. In multivariate statistical analysis, elliptical distributions have recently provided an alternative to the normal model.Elliptical distributions have also increased their popularity in f inance because of the ability to model heavy tails usually observed in real data. Most of the work, however, is spread out in journals throughout the world and is noteasily accessible to the investigators. A noteworthy function of this book is the collect ion of the most important results on the theory of matrix variate elliptically contoured distributions that were previously only available in thejournal-based literature. The content is organized in a unified manner that can serve an a valuable introducti on to the subject
Note:Springer eBooks
Contents:Preliminaries
Basic Properties
Probability Density Function and Expected Values
Mixtures of Normal Distributions
Quadratic Forms and other Functions of Elliptically Contoured Matrices
Characterization Results
Estimation
Hypothesis Testing
Linear Models
Skew Elliptically Contoured Distributions
Application in Portfolio Theory
Author Index
Subject Index
ISBN:9781461481546
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Statistics , Mathematical statistics , Economics Statistics
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Call number:SPRINGER-2013-9781461471967:ONLINE Show nearby items on shelf
Title:Measure, Integral, Derivative [electronic resource] : A Course on Lebesgue's Theory
Author(s): Sergei Ovchinnikov
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:This classroom-tested text is intended for a one-semester course in Lebesgues theory. With over 180 exercises, the texttakes an elementary approach, making iteasily accessible toboth upper-undergraduate- andlower-graduate-level students. The three ma in topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis. In order to keep the book self-contained, anintroductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiabilityproperty of functions of bounded variations, are dissected into small steps in order to be accessi ble to students. With the exception of a few simple statements, all results are proven in the text. The presentation is elementary,where -algebras are not used in the text on measure theory and Dinis derivatives are not used in the chapter on differentiat ion. However, all the main results of Lebesgues theory are found in the book
Note:Springer eBooks
Contents:1 Preliminaries
2 Lebesgue Measure
3 Lebesgue Integration
4 Differentiation and Integration
A Measure and Integral over Unbounded Sets
Index
ISBN:9781461471967
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics)
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Call number:SPRINGER-2013-9781461471936:ONLINE Show nearby items on shelf
Title:Lie Groups: Structure, Actions, and Representations [electronic resource] : In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday
Author(s): Alan Huckleberry
Ivan Penkov
Gregg Zuckerman
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:Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profoundcontributions to mathematics. D ue to Professor Wolfs broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric, and analytic methods areemployed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representationspaces are discussed. Contributions in the area of representation theory involve numero us viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis. Contributors D. Akhiezer T. Oshima A. Andrada I. Pacharoni M. L. Barberis F. Ricci L. Barchini S. Rosenberg I. Dotti N. Shimeno M. Eastwood J. Tirao V . Fischer S. Treneer T. Kobayashi C.T.C. Wall A. Kornyi D. Wallace B. Kostant K. Wiboonton P. Kostelec F. Xu K.-H. Neeb O. Yakimova G. Olafsson R. Zierau B. rsted
Note:Springer eBooks
Contents:Preface
Real group orbits on flag manifolds
Complex connections with trivial holonomy
Indefinite harmonic theory and harmonic spinors
Twistor theory and the harmonic hull
Nilpotent Gelfand pairs and spherical transforms of Schwartz functions, II: Taylor expansions on singular sets
Propagation of the multiplicity
freeness property for holomorphic vector bundles
Poisson transforms for line bundles from the Shilov boundary to bounded symmetric domains
Cent(U(n)), cascade of orthogonal roots, and a construction of LipsmanWolf
Weakly harmonic Maa forms and the princi
ISBN:9781461471936
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v306
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Functional analysis
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Call number:SPRINGER-2013-9781461469469:ONLINE Show nearby items on shelf
Title:Applications of q-Calculus in Operator Theory [electronic resource]
Author(s): Ali Aral
Vijay Gupta
Ravi P Agarwal
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:Springer 2013 e-book collections
Note:The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas suchas computer-aided geometric design, numericalanalysis, and solutions of dif ferential equations. q-Calculus is a generalization of many subjects, such as hypergeometric series, complex analysis, and particle physics. This monograph is an introduction to combining approximationtheory and q-Calculus with applications, by usingwell- known operators. The presentation is systematic and the authors include a brief summary of the notations and basicdefinitions ofq-calculus before delving into more advancedmaterial. Themany applications of q-calculus in the theory of approximation, espec ially onvariousoperators,which includes convergence of operators to functions in real and complex domain forms the gist of the book. This book issuitable for researchers andstudents in mathematics,physics andengineering,and forprofessionals who would enjo y exploring the host of mathematicaltechniques and ideas that are collected and discussedin thebook
Note:Springer eBooks
Contents:Introduction of q
calculus
q
Discrete operators and their results
q
Integral operators
q
Bernstein type integral operators
q
Summation
integral operators
Statistical convergence of q
operators
q
Complex operators
ISBN:9781461469469
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Functions of complex variables
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Call number:SPRINGER-2013-9781461459811:ONLINE Show nearby items on shelf
Title:The Implicit Function Theorem [electronic resource] History, Theory, and Applications
Author(s): Steven G Krantz
Harold R Parks
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
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Note:The implicit function theorem is part ofthe bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theoremshave now blossomed into p owerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classicalformulation forCkfunctions, (ii) formulations in ot her function spaces, (iii) formulations for non-smooth functions, and (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems,such as the NashMoser theorem, have been developed for specific applications ( e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present uncorrected reprint of thisclassicmonograph. Originally published in 2002,The Implicit Function Theoremis an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians,graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in mo dern mathematics. It serves to document and placein context a substantial body ofmathematical ideas
Note:Springer eBooks
Contents:Preface
Introduction to the Implicit Function Theorem
History
Basic Ideas
Applications
Variations and Generalizations
Advanced Implicit Function Theorems
Glossary
Bibliography
Index
ISBN:9781461459811
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Differential Equations , Differential equations, partial , Global differential geometry
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Call number:SPRINGER-2013-9781461459620:ONLINE Show nearby items on shelf
Title:Foundations of Abstract Analysis [electronic resource]
Author(s): Jewgeni H Dshalalow
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
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Note:Foundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presentedin a self-contained wa y suitable both for classroom use and for self-study. While this book carries the rigor of advancedmodern analysis texts, it elaborates the material in much greater details and therefore fills a gap betweenintroductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience. To relieve the reader of thepotential overload of new words, definitions, and concepts, the book (in its u nique feature) provides lists of new terms at the end of each section, in a chronological order. Difficult to understand abstract notions are preceded byinformal discussions and blueprints followed by thorough details andsupported by examples and figures. To further reinforce the text, hints and solutions to almost a half of more than 580 problems are provided at the end of thebook, still leaving ample exercises for assignments. This volume covers topics in point-set topology and measure and integration. P rerequisites include advanced calculus, linear algebra, complex variables, and calculus basedprobability
Note:Springer eBooks
Contents:Set
Theoretic and Algebraic Preliminaries
Analysis of Metric Spaces
Elements of Point
Set Topology
Measurable Spaces and Measurable Functions
Measures
Integration in Abstract Spaces
Solutions to Selected Problems
Bibliography
List of Symbols
Index of Names and Terms
ISBN:9781461459620
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functional analysis , Numerical analysis
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Call number:SPRINGER-2013-9781461457251:ONLINE Show nearby items on shelf
Title:Hidden HarmonyGeometric Fantasies [electronic resource] : The Rise of Complex Function Theory
Author(s): Umberto Bottazzini
Jeremy Gray
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:Hidden HarmonyGeometric Fantasies describes the history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted tocomplex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subjectCauchy, Riemann, and Weierstrassit looks at thecontributions of great mathematicians from dAlembert to Po incar, and Laplace to Weyl. Select chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric functiontheory, and the early years of complex function theory in several variables. Unique em phasis has been placed on the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages.This book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture o f the broad cultural and social context in which the main players lived and worked by paying attention to the rise ofmathematical schools and of contrasting national traditions. This work is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It is a major resource for professionalmathematicians as well as advanced undergraduate and graduate students and anyone studying complex function theory
Note:Springer eBooks
Contents:List of Figures
Introduction
1. Elliptic Functions
2. From real to complex
3. Cauch
4. Elliptic integrals
5. Riemann
6. Weierstrass
7. Differential equations
8. Advanced topics
9. Several variables
10. Textbooks
ISBN:9781461457251
Series:e-books
Series:SpringerLink (Online service)
Series:Sources and Studies in the History of Mathematics and Physical Sciences
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Functions of complex variables , Number theory
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Call number:SPRINGER-2013-9781461452577:ONLINE Show nearby items on shelf
Title:Real and Convex Analysis [electronic resource]
Author(s): Erhan nlar
Robert J Vanderbei
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:This book offers a first course in analysis for scientists and engineers. It can be used at the advanced undergraduate level or as part of the curriculum in a graduate program. The book is built around metric spaces. Inthe first three chapters, the authors lay the foundational material and cover the all-important four-Cs: convergence, completeness, compactness, and continuity.In subsequent chapters, the basic tools of analysis are used togive brief introductions to differential and integralequations , convex analysis, and measure theory. The treatment is modern and aesthetically pleasing. The book contains detailed illustrations, examples and exercises. It laysthe groundwork for the needs of classical fields as well as the important new fields of op timization and probability theory
Note:Springer eBooks
Contents:Sets and Functions
Metric Spaces
Functions on Metric Spaces
Differential and Integral Equations
Convexity
Convex Optimization
Measure and Integration
Bibiography
Index
ISBN:9781461452577
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Mathematical optimization , Engineering mathematics
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Call number:SPRINGER-2013-9781461436317:ONLINE Show nearby items on shelf
Title:A Logical Introduction to Proof [electronic resource]
Author(s): Daniel W Cunningham
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:A Logical Introduction to Proof is a unique textbook that uses a logic-first approach to train and guide undergraduates through a transition or bridge course between calculus and advanced mathematics courses. Theauthors approach prepares the student for the rigors required in future mathematics courses and is appropriate for majors in mathematics, computer science, engineering, as well as other applied mathematical sciences. It may alsobe beneficial as a supplement for students at the graduate level who need guidance or reference for writing proofs. Core topics covered are logic, sets, relations, functions, and induction, where logic is the instrument foranalyzing the structure of mathematical assertions and is a tool for composing mathematical proof s. Exercises are given at the end of each section within a chapter. Chapter 1 focuses on propositional logic while Chapter 2 is devoted tothe logic of quantifiers. Chapter 3 methodically presents the key strategies that are used in mathematical proofs eac h presented as a proof diagram. Every proof strategy is carefully illustrated by a variety of mathematical theoremsconcerning the natural, rational, and real numbers. Chapter 4 focuses on mathematical induction and concludes with a proof of the fundamenta l theorem of arithmetic. Chapters 5 through 7 introduce students to the essential concepts thatappear in all branches of mathematics. Chapter 8 introduces the basic structures of abstract algebra: groups, rings, quotient groups, and quotient rings. Finall y, Chapter 9 presents proof strategies that explicitly show students how todeal with the fundamental definitions that they will encounter in real analysis, followed by numerous examples of proofs that use these strategies. The appendix provides a useful s ummary of strategies for dealing with proofs
Note:Springer eBooks
Contents:Preface
The Greek Alphabet
1. Propositional Logic
2. Predicate Logic
3. Proof Strategies and Diagrams
4. Mathematical Induction
5. Set Theory
6. Functions
7. Relations
8. Core Concepts in Abstract Algebra
9. Core Concepts in Real Analysis
A Summary of Strategies
References
List of Symbols. Index
ISBN:9781461436317
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical
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Call number:SPRINGER-2013-9781447151227:ONLINE Show nearby items on shelf
Title:Real Analysis: Measures, Integrals and Applications [electronic resource]
Author(s): Boris Makarov
Anatolii Podkorytov
Date:2013
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
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Note:Real Analysis: Measures, Integrals and Applications is devoted to the basics of integration theory and its related topics. The main emphasis is made on the properties of the Lebesgue integral and various applications bothclassical and those rarely co vered in literature. This book provides a detailed introduction to Lebesgue measure and integration as well as the classical results concerning integrals of multivariable functions. It examines theconcept of the Hausdorff measure, the properties of the a rea on smooth and Lipschitz surfaces, the divergence formula, and Laplace's method for finding the asymptotic behavior of integrals. The general theory is then applied toharmonic analysis, geometry, and topology. Preliminaries are provided on probability theory, including the study of the Rademacher functions as a sequence of independent random variables. The book contains more than 600 examples andexercises. The reader who has mastered the first third of the book will be able to study other areas of mat hematics that use integration, such as probability theory, statistics, functional analysis, partial probability theory,statistics, functional analysis, partial differential equations and others. Real Analysis: Measures, Integrals and Applications is inte nded for advanced undergraduate and graduate students in mathematics and physics. It assumes thatthe reader is familiar with basic linear algebra and differential calculus of functions of several variables
Note:Springer eBooks
Contents:Measure
The Lebesgue Model
Measurable Functions
The Integral
The Product Measure
Change of Variables in an Integral
Integrals Dependent on a Parameter
Surface Integrals
Approximation and Convolution of the Space
Fourier Series and the Fourier Transform
Charges. The Radon
Nikodym Theory
Integral Representation of Linear Functionals
Appendices
ISBN:9781447151227
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Geometry
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Call number:SPRINGER-2013-9780817684037:ONLINE Show nearby items on shelf
Title:Lectures on Constructive Approximation [electronic resource] : Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball
Author(s): Volker Michel
Date:2013
Publisher:Boston : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises theauthors lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide thefoundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as themodeling of the Earths or the brains interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, andballs * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelets an d scaling functions This textbook is written for students in mathematics, physics, engineering, and the geosciences who have abasic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the ab ove-mentioned fields
Note:Springer eBooks
Contents:Introduction: the Problem to be Solved
Part I Basics
Basic FundamentalsWhat You Need to Know
Approximation of Functions on the Real Line
Part II Approximation on the Sphere
Basic Aspects
Fourier Analysis
Spherical Splines
Spherical Wavelet Analysis
Spherical Slepian Functions
Part III Approximation on the 3D Ball
Orthonormal Bases
Splines
Wavelets for Inverse Problems on the 3D Ball
The Regularized Functional Matching Pursuit (RFMP)
References
Index
ISBN:9780817684037
Series:e-books
Series:SpringerLink (Online service)
Series:Applied and Numerical Harmonic Analysis
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Functions, special , Numerical analysis , Mathematical physics
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Call number:SPRINGER-2012-9789491216442:ONLINE Show nearby items on shelf
Title:Analytic Inequalities [electronic resource] : Recent Advances
Author(s): B.G Pachpatte
Date:2012
Publisher:Paris : Atlantis Press
Size:1 online resource
Note:Springer e-book platform
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Note:For more than a century, the study of various types of inequalities has been the focus of great attention by many researchers, interested both in the theory and its applications. In particular, there exists a very rich literaturerelated to the well k nown Cebysev, Gruss, Trapezoid, Ostrowski, Hadamard and Jensen type inequalities. The present monograph is an attempt to organize recent progress related to the above inequalities, which we hope will widen thescope of their applications. The field to be c overed is extremely wide and it is impossible to treat all of these here. The material included in the monograph is recent and hard to find in other books. It is accessible to any readerwith a reasonable background in real analysis and an acquaintance wit h its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves awarm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be invaluable reading for mathematicians and engineers and also for graduate students, scientists andscholars wishing to keep abreast of this important area of research
Note:Springer eBooks
Contents:Grss
and ebyev
type inequalities
Multidimensional Grss
ebyev and
Trapezoid
type inequalities
Ostrowski
type inequalities
Multidimensional Ostrowski
type inequalities
Inequalities via convex functions
ISBN:9789491216442
Series:e-books
Series:SpringerLink (Online service)
Series:Atlantis Studies in Mathematics, 1875-7634 : v3
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics
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Call number:SPRINGER-2012-9788876424434:ONLINE Show nearby items on shelf
Title:An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs [electronic resource]
Author(s): Mariano Giaquinta
Luca Martinazzi
Date:2012
Publisher:Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale
Size:1 online resource
Note:Springer e-book platform
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Note:This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress ofMathematicians in 1900 in Paris: 19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic? 20th problem: does any variational problem have a solution, provided that certainassumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended? During the last century these two problems have generated a great deal of work, usually referred to asregularity theory, which makes this topic quite relevant in many fields and still very active for research. However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to illustrate only some of thebasic ideas and techniques introduced in this context, confining ourselves to important but simpl e situations and refraining from completeness. In fact some relevant topics are omitted. Topics include: harmonic functions, directmethods, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and Lp-theory both with and without potential theory, including the Calderon-Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar caseand partial regularity theorems in the vector valued case energy minimizing harmonic maps and minimal graphs in codimension 1 and greater than 1. In this second deeply revised edition we also included the regularity of 2-dimensionalweakly harmonic maps, the partial regularity of stationary harmonic maps, and their connections with the case p=1 of theLp theory, including the celebrated results of W ente and of Coifman-Lions-Meyer-Semmes
Note:Springer eBooks
Contents:1 Harmonic functions
2 Direct methods
3 Hilbert space methods
4 L2
regularity: the Caccioppoli inequality
5 Schauder estimates
6 Some real analysis
7 Lp
theory
8 The regularity problem in the scalar case
9 Partial regularity in the vector
valued case
10 Harmonic maps
11 A survey of minimal graphs
ISBN:9788876424434
Series:e-books
Series:SpringerLink (Online service)
Series:Publications of the Scuola Normale Superiore
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial
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Call number:SPRINGER-2012-9783642298493:ONLINE Show nearby items on shelf
Title:Geometric Aspects of Functional Analysis [electronic resource] : Israel Seminar 20062010
Author(s): Bo'az Klartag
Shahar Mendelson
Vitali D Milman
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) from the years 2006 to 2011 continues the long tradition of the previous volumes, which reflect the generaltrends of Asymptotic Geome tric Analysis, understood in a broad sense, and are a source of inspiration for new research. Most of the papers deal with various aspects of the theory, including classical topics in the geometry of convexbodies, inequalities involving volumes of such bo dies or more generally, logarithmically-concave measures, valuation theory, probabilistic and isoperimetric problems in the combinatorial setting, volume distribution on high-dimensionalspaces and characterization of classical constructions in Geometry an d Analysis (like the Legendre and Fourier transforms, derivation and others). All the papers here are original research papers
Note:Springer eBooks
Contents:The
Cosine Transform and Intertwining Integrals on Real Grassmannians
On Modules Over Valuations
On Multiplicative Maps of Continuous and Smooth Functions
Order Isomorphisms on Convex Functions in Windows
Finite Transitive Graph Embeddings into a Hyperbolic
Metric Space Must Stretch or Squeeze
Tightness of Fluctuations of First Passage Percolation on Some Large Graphs
Finitely Supported Measures on SL2(R) which are Absolutely Continuous at Infinity
Interpolations, Convexity and Geometric Inequalities
Hypercontractive Measures, Talagrand's Inequality, and Inuences
ISBN:9783642298493
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2050
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Discrete groups , Distribution (Probability theory)
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Call number:SPRINGER-2012-9783034803465:ONLINE Show nearby items on shelf
Title:Recent Progress in Operator Theory and Its Applications [electronic resource]
Author(s): Joseph A Ball
Ral E Curto
Sergei M Grudsky
J. William Helton
Ral Quiroga-Barranco
Nikolai L Vasilevski
Date:2012
Publisher:Basel : Springer Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume contains twenty-one solicited articles by speakers at the IWOTA 2009 workshop, ranging from expository surveys to original research papers, each carefully refereed.The contributions reflect recent developments inoperator theory and its ap plications. Consistent with the topics of recent IWOTA meetings, IWOTA 2009 was designed as a comprehensive, inclusive conference covering all aspects of theoretical and applied operator theory, ranging fromclassical analysis, differential and integral eq uations, complex and harmonic analysis to mathematical physics, mathematical systems and control theory, signal processing and numerical analysis. The conference brought togetherinternational experts for a week-long stay at Hotel Real de Minas, in an atmo sphere conducive to fruitful, professional interactions. These proceedings reflect the high quality of the papers presented at the conference
Note:Springer eBooks
ISBN:9783034803465
Series:e-books
Series:SpringerLink (Online service)
Series:Operator Theory: Advances and Applications : v220
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Functions of complex variables , Operator theory , Differential equations, partial
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Call number:SPRINGER-2012-9783034801805:ONLINE Show nearby items on shelf
Title:Visual Complex Functions [electronic resource] : An Introduction with Phase Portraits
Author(s): Elias Wegert
Date:2012
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations so-called phase portraits which visualize functions as images ontheir domains. Reading Visua l Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course oncomplex analysis. With separate chapters on variou s construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes. In a second storyline,running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endowindividual faces to analytic functions. Phase portraits enhance the intuitive understanding of conc epts in complex analysis and are expected to be useful tools for anybody working with special functions even experienced researchersmay be inspired by the pictures to new and challenging questions. Visual Complex Functions may also serve as a companion t o other texts or as a reference work for advanced readers who wish to know more about phase portraits
Note:Springer eBooks
Contents:Preface
1. Getting Acquainted
2. Complex Functions
3. Analytic Functions
4. Complex Calculus
5. Construction Principles
6. Conformal Mappings
7. Riemann Surfaces
ISBN:9783034801805
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables , Functions, special
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
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