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SPIRES-BOOKS: FIND KEYWORD FUNCTIONS OF REAL VARIABLES *END*INIT* use /tmp/qspiwww.webspi1/8403.22 QRY 131.225.70.96 . find keyword functions of real variables ( 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-2016-9783319307442: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-2016-9783319281063: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-2016-9783319273235: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-2014-9783319062099: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-2014-9783034806220: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-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
Note:Springer e-book platform
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-2013-9781461459620: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
Note:Springer 2013 e-book collections
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
Note:Springer e-book platform
Note:Springer 2013 e-book collections
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-2013-9781447151227: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
Note:Springer 2013 e-book collections
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-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
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Call number:SPRINGER-2012-9781441988010:ONLINE Show nearby items on shelf
Title:Analysis on Fock Spaces [electronic resource]
Author(s): Kehe Zhu
Date:2012
Publisher:Boston, MA : Springer US : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Several natural Lp spaces of analytic functions have been widely studied in the past few decades, including Hardy spaces, Bergman spaces, and Fock spaces. The terms Hardy spaces and Bergman spaces are by now standardand well established. But the term Fock spaces is a different story. Numerous excellent books now exist on the subject of Hardy spaces. Several books about Bergman spaces, including some of the authors, have also appeared inthe past few decades. But there has been no book on the market co ncerning the Fock spaces. The purpose of this book is to fill that void, especially when many results in the subject are complete by now. This book presents importantresults and techniques summarized in one place, so that newcomers, especially graduate st udents, have a convenient reference to the subject. This book contains proofs that are new and simpler than the existing ones in the literature.In particular, the book avoids the use of the Heisenberg group, the Fourier transform, and the heat equation. T his helps to keep the prerequisites to a minimum. A standard graduate course in each of real analysis, complex analysis, andfunctional analysis should be sufficient preparation for the reader
Note:Springer eBooks
Contents:Preface
Chapter 1. Preliminaries
Chapter 2. Fock Spaces
Chapter 3. The Berezin Transform and BMO
Chapter 4. Interpolating and Sampling Sequences
Chapter 5. Zero Sets for Fock Spaces
Chapter 6. Toeplitz Operators
Chapter 7. Small Hankel Operators
Chapter 8. Hankel Operators
References
Index
ISBN:9781441988010
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v263
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-2011-9788876423864:ONLINE Show nearby items on shelf
Title:Introduction to Measure Theory and Integration [electronic resource]
Author(s): Luigi Ambrosio
Giuseppe Prato
Andrea Mennucci
Date:2011
Publisher:Pisa : Edizioni della Normale
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This textbook collects the notes for an introductory course in measure theory and integration. The course was taught by the authors to undergraduate students of the Scuola Normale Superiore, in the years 2000-2011. The goal of thecourse was to presen t, in a quick but rigorous way, the modern point of view on measure theory and integration, putting Lebesgue's Euclidean space theory into a more general context and presenting the basic applications to Fourierseries, calculus and real analysis. The text can also pave the way to more advanced courses in probability, stochastic processes or geometric measure theory. Prerequisites for the book are a basic knowledge of calculus in one andseveral variables, metric spaces and linear algebra. All results presen ted here, as well as their proofs, are classical. The authors claim some originality only in the presentation and in the choice of the exercises. Detailed solutionsto the exercises are provided in the final part of the book
Note:Springer eBooks
Contents:Measure spaces
Integration
Spaces of measurable functions
Hilbert spaces
Fourier series
Operations on measures
The fundamental theorem of integral calculus
Operations on measures
Appendix: Riesz representation theorem of the dual of C(K) and integrals depending on a parameter
Solutions to the exercises
ISBN:9788876423864
Series:e-books
Series:SpringerLink (Online service)
Series:Appunti/Lecture Notes : v10
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics
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Call number:SPRINGER-2011-9788847016798:ONLINE Show nearby items on shelf
Title:Wiener Chaos: Moments, Cumulants and Diagrams [electronic resource] : A survey with computer implementation
Author(s): Giovanni Peccati
Murad S Taqqu
Date:2011
Publisher:Milano : Springer Milan
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The concept of Wiener chaos generalizes to an infinite-dimensional setting the properties of orthogonal polynomials associated with probability distributions on the real line. It plays a crucial role in modern probability theory,with applications ran ging from Malliavin calculus to stochastic differential equations and from probabilistic approximations to mathematical finance. This book is concerned with combinatorial structures arising from the study ofchaotic random variables related to infinitely d ivisible random measures. The combinatorial structures involved are those of partitions of finite sets, over which Mbius functions and related inversion formulae are defined. Thiscombinatorial standpoint (which is originally due to Rota and Wallstrom) pro vides an ideal framework for diagrams, which are graphical devices used to compute moments and cumulants of random variables. Several applications aredescribed, in particular, recent limit theorems for chaotic random variables. An Appendix presents a comp uter implementation in MATHEMATICA for many of the formulae
Note:Springer eBooks
ISBN:9788847016798
Series:e-books
Series:SpringerLink (Online service)
Series:Bocconi & Springer Series, 2039-1471 : v1
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Combinatorics , Distribution (Probability theory)
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Call number:SPRINGER-2011-9783642174131:ONLINE Show nearby items on shelf
Title:Computational Approach to Riemann Surfaces [electronic resource]
Author(s): Alexander I Bobenko
Christian Klein
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically availablenumerical codes in this fie ld. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory arepresented. The intended audience of this book is twofol d. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, isrequired. In particular, no knowledge of the theory of Riemann surfaces is exp ected the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists ingeometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the f irst book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it containsoriginal results. There are a growing number of applications that involve the evaluation of concrete characteristics of models a nalytically described in terms of Riemann surfaces. Many problem settings and computations in this volumeare motivated by such concrete applications in geometry and mathematical physics
Note:Springer eBooks
Contents:Introduction to Compact Riemann Surfaces
Computing with plane algebraic curves and Riemann surfaces: the algorithms of the Maple package algcurves
Algebraic curves and Riemann surfaces in Matlab
Computing Poincar Theta Series for Schottky Groups
Uniformizing real hyperelliptic M
curves using the Schottky
Klein prime function
Numerical Schottky Uniformizations: Myrbergs Opening Process
Period Matrices of Polyhedral Surfaces
On the spectral theory of the Laplacian on compact polyhedral surfaces of arbitrary genus
ISBN:9783642174131
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2013
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Functions of complex variables , Numerical analysis
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Call number:SPRINGER-2011-9783642129094:ONLINE Show nearby items on shelf
Title:Value Distribution of Meromorphic Functions [electronic resource]
Author(s): Jianhua Zheng
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:Value Distribution of Meromorphic Functions focuses on functions meromorphic in an angle or on the complex plane, T directions, deficient values, singular values, potential theory in value distribution and the proof of thecelebrated Nevanlinna conjec ture. The book introduces various characteristics of meromorphic functions and their connections, several aspects of new singular directions, new results on estimates of the number of deficient values, newresults on singular values and behaviours of subha rmonic functions which are the foundation for further discussion on the proof of the Nevanlinna conjecture. The independent significance of normality of subharmonic function family isemphasized. This book is designed for scientists, engineers and post gra duated students engaged in Complex Analysis and Meromorphic Functions. Dr. Jianhua Zheng is a Professor at the Department of Mathematical Sciences, TsinghuaUniversity, China
Note:Springer eBooks
Contents:Preliminaries of Real Functions
Characteristics of a Meromorphic Function
T Directions of a Meromorphic Function
Argument Distribution and Deficient Values
Meromorphic Functions With Radially Distributed Values
Singular Values of Meromorphic Functions
The Potential Theory in Value Distribution
ISBN:9783642129094
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functions of complex variables
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Call number:SPRINGER-2011-9781461414995:ONLINE Show nearby items on shelf
Title:Hamiltonian Structures and Generating Families [electronic resource]
Author(s): Sergio Benenti
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is an enhanced version of an earlier Russian edition. Besides thorough revisions, more emphasis was put on reordering the topics according to a category-theoretical view. This allows the mathematical results to bestated, proved, and underst ood in a much easier and elegant way. From the reviews of the Russian edition: The main accent is shifted to the application. . .in geometrical optics, thermostatics and control theory, and not to theHamiltonian mechanics only. . . . To make the book fair ly self-contained, full details of basic definitions and all proofs are included. In this way, the majority of the text can be read without the prerequisite of a course ingeometry. The excellent collection of examples illustrates the relatively hard and h ighly abstract mathematical theory and its hidden difficulties.. . .The book can rise real interest for specialists . . . . The . . . book is asignificant input in the modern symplectic geometry and its applications. (Andrey Tsiganov, St. Petersburg State University) Sergio Benenti is a professor of mathematical physics at Universit di Torino, Italy. His current fields ofresearch include symplectic geometry with applications to physical theories, Riemannian geometry with applications to the theory of the separation of variables in the Hamilton-Jacobi equation and in other relevant differentialequations of physics, and mathematical models of the dynamics of non-holonomic systems
Note:Springer eBooks
Contents:Preface
Basic Notions of Calculus on Manifolds
Relations
Symplectic Relations on Symplectic Manifolds
Symplectic Relations on Cotangent Bundles
Canonical Lift on Cotangent Bundles
The Geometry of the Hamilton
Jacobi Equation
Hamiltonian Optics in Euclidean Spaces
Control of Static Systems
Supplementary Topics
Global Hamilton Principal Functions on S2 and H2
References
Index
ISBN:9781461414995
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Systems theory , Global differential geometry
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Call number:SPRINGER-2011-9781441998132:ONLINE Show nearby items on shelf
Title:Nonelliptic Partial Differential Equations [electronic resource] : Analytic Hypoellipticity and the Courage to Localize High Powers of T
Author(s): David S Tartakoff
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book fills a real gap in the analytical literature. After many years and many results of analytic regularity for partial differential equations, the only access to the technique known as $(T^p)_\phi$ has remained embedded inthe research papers t hemselves, making it difficult for a graduate student or a mature mathematician in another discipline to master the technique and use it to advantage. This monograph takes a particularly non-specialist approach,one might even say gentle, to smoothly bring the reader into the heart of the technique and its power, and ultimately to show many of the results it has been instrumental in proving. Another technique developed simultaneously by F.Treves is developed and compared and contrasted to ours. The techni ques developed here are tailored to proving real analytic regularity to solutions of sums of squares of vector fields with symplectic characteristic variety andothers, real and complex. The motivation came from the field of several complex variables and t he seminal work of J. J. Kohn. It has found application in non-degenerate (strictly pseudo-convex) and degenerate situations alike, linearand non-linear, partial and pseudo-differential equations, real and complex analysis. The technique is utterly elemen tary, involving powers of vector fields and carefully chosen localizing functions. No knowledge of advancedtechniques, such as the FBI transform or the theory of hyperfunctions is required. In fact analyticity is proved using only $C^\infty$ techniques. The book is intended for mathematicians from graduate students up, whether inanalysis or not, who are curious which non-elliptic partial differential operators have the property that all solutions must be real analytic. Enough background is provided to pr epare the reader with it for a clear understanding of thetext, although this is not, and does not need to be, very extensive. In fact, it is very nearly true that if the reader is willing to accept
Note:Springer eBooks
Contents:1. What this book is and is not
2. Brief Introduction
3.Overview of Proofs
4. Full Proof for the Heisenberg Group
5. Coefficients
6. Pseudo
differential Problems
7. Sums of Squares and Real Vector Fields
8. \bar{\partial}
Neumann and the Boundary Laplacian
9. Symmetric Degeneracies
10. Details of the Previous Chapter
11. Non
symplectic Strategem ahe
12.Operators of Kohn Type Which Lose Derivatives
13. Non
linear Problems
14. Treves' Approach
15. Appendix
Bibliography
ISBN:9781441998132
Series:e-books
Series:SpringerLink (Online service)
Series:Developments in Mathematics, 1389-2177 : v22
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Differential equations, partial
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Call number:SPRINGER-2010-9788847017849:ONLINE Show nearby items on shelf
Title:Mathematical Analysis II [electronic resource]
Author(s): Claudio Canuto
Anita Tabacco
Date:2010
Publisher:Milano : Springer Milan
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The purpose of this textbook is to present an array of topics in Calculus, and conceptually follow our previous effort Mathematical Analysis I.The present material is partly found, in fact, in the syllabus of the typical secondlecture course in Calcu lus as offered in most Italian universities. While the subject matter known as `Calculus 1' is more or less standard, and concerns real functions of real variables, the topics of a course on `Calculus 2'can varya lot, resulting in a bigger flexibility. Fo r these reasons the Authors tried to cover a wide range of subjects, not forgetting that the number of credits the current programme specifications confers to a second Calculus course is notcomparable to the amount of content gathered here. The reminders disseminated in the text make the chapters more independent from one another, allowing the reader to jump back and forth, and thus enhancing the versatility of the book.On the website: http://calvino.polito.it/canuto-tabacco/analisi 2, the interested read er may find the rigorous explanation of the results that are merely stated without proof in the book, together with useful additional material. TheAuthors have completely omitted the proofs whose technical aspects prevail over the fundamental notions and ideas. The large number of exercises gathered according to the main topics at the end of each chapter should help the studentput his improvements to the test. The solution to all exercises is provided, and very often the procedure for solving is outlined
Note:Springer eBooks
ISBN:9788847017849
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functional analysis , Differential Equations , Differential equations, partial
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Call number:SPRINGER-2010-9783642148286:ONLINE Show nearby items on shelf
Title:Symmetries of Compact Riemann Surfaces [electronic resource]
Author(s): Emilio Bujalance
Francisco Javier Cirre
Jos Manuel Gamboa
Grzegorz Gromadzki
Date:2010
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This monograph deals with symmetries of compact Riemann surfaces. A symmetry of a compact Riemann surface S is an antianalytic involution of S. It is well known that Riemann surfaces exhibiting symmetry correspond to algebraiccurves which can be defi ned over the field of real numbers. In this monograph we consider three topics related to the topology of symmetries, namely the number of conjugacy classes of symmetries, the numbers of ovals of symmetries andthe symmetry types of Riemann surfaces
Note:Springer eBooks
Contents:1 Preliminaries
2 Number of Conjugacy Classes of Symmetries
3 Counting Ovals of Symmetries
4 Symmetry Types of some Families of Riemann Surfaces
5 Symmetry Types of Riemann Surfaces with a Large Group of Automorphisms
6 Appendix
ISBN:9783642148286
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2007
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Group theory , Functions of complex variables , Topology
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Call number:SPRINGER-2010-9781441991263:ONLINE Show nearby items on shelf
Title:Discrete Integrable Systems [electronic resource] : QRT Maps and Elliptic Surfaces
Author(s): J.J Duistermaat
Date:2010
Edition:1
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The rich subject matter in this book brings in mathematics from different domains, especially from the theory of elliptic surfaces and dynamics.The material comes from the authors insights and understanding of a birationaltransformation of the plane derived from a discrete sine-Gordon equation, posing the question of determining the behavior of the discrete dynamical system defined by the iterates of the map. The aim of this book is to give a completetreatment not only of the basic facts about QRT ma ps, but also the background theory on which these maps are based. Readers with a good knowledge of algebraic geometry will be interested in Kodairas theory of elliptic surfaces andthe collection of nontrivial applications presented here. While prerequisit es for some readers will demand their knowledge of quite a bit of algebraic- and complex analytic geometry, different categories of readers will be able tobecome familiar with any selected interest in the book without having to make an extensive journey t hrough the literature
Note:Springer eBooks
Contents:The QRT Map
The Pencil of Biquadratic Curves in
The QRT surface
Cubic Curves in the Projective Plane
The Action of the QRT Map on Homology
Elliptic Surfaces
Automorphisms of Elliptic Surfaces
Elliptic Fibrations with a Real Structure
Rational elliptic surfaces
Symmetric QRT Maps
Examples from the Literature
Appendices
ISBN:9781441991263
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Functions of complex variables , Number theory
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Call number:SPRINGER-2010-9781441973320:ONLINE Show nearby items on shelf
Title:Advanced Calculus [electronic resource] : A Geometric View
Author(s): James J Callahan
Date:2010
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit andinverse function theore ms, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincar lemma. The ideas behind most topics can be understood withjust two or three variables. This invites geome tric visualization the book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements ofthe calculus of differentiable maps, such as the role of the derivativ e as the local linear approximation to a map and its role in the change of variables formula for multiple integrals. The geometric theme continues with an analysisof the physical meaning of the divergence and the curl at a level of detail not found in oth er advanced calculus books. Advanced Calculus: A Geometric View is a textbook for undergraduates and graduate students in mathematics, thephysical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. The re is enough material for a year-long course on advanced calculus and for a variety of semester courses--includingtopics in geometry. It avoids duplicating the material of real analysis. The measured pace of the book, with its extensive examples and illus trations, make it especially suitable for independent study
Note:Springer eBooks
Contents:1. Starting Points
2. Geometry of Linear Maps
3. Approximations
4. The Derivative
5. Inverses
6. Implicit Functions
7. Critical Points
8. Double Integrals
9. Evaluating Double Integrals
10. Sufrace Integrals
11. Stokes' Theorem
ISBN:9781441973320
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)
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Call number:SPRINGER-2010-9781441909169:ONLINE Show nearby items on shelf
Title:The H-Function [electronic resource] Theory and Applications
Author(s): A.M Mathai
Ram Kishore Saxena
Hans J Haubold
Date:2010
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The topics of special H-function and fractional calculus are currently undergoing rapid changes both in theory and application. Taking into account the latest research results, the authors delve into these topics as they relateto applications to prob lems in statistics, physics, and engineering, particularly in condensed matter physics, plasma physics, and astrophysics. The book sets forth the definitions, contours, existence conditions, and particular casesfor the H-function, then explores the proper ties and relationships among the Laplace, Fourier, Hankel, and other transforms. From here, the H-functions are utilized for applications in statistical distribution theory, structures ofrandom variables, generalized distributions, Mathais pathway models, and versatile integrals. Functions of matrix argument are introduced with a focus on real-valued scalar functions when the matrices are real or Hermitianpositive-definite. The text concludes with important recent applications to physical problems in reac tion, diffusion, reaction-diffusion theory and statistics, and superstatistics. Generalized entropies as well as applications inastrophysics are dealt with. Over the last few years, material in this book has been added to various courses and developed to meet the needs of scholars at the PhD level. All exercises in the book have been used to probe the knowledgeand ability of mathematics, statistics, and physics to students and researchers
Note:Springer eBooks
Contents:On The H
Function with Applications
H
Function in Science and Engineering
Fractional Calculus
Applications in Statistics
Functions of Matrix Argument
Applications in Astrophysics Problems
Glossary
Author Index
Subject Index
ISBN:9781441909169
Series:e-books
Series:SpringerLink (Online service)
Series:Physics and Astronomy (Springer-11651)
Keywords: Functions, special , Mathematical physics , Mathematical statistics , Engineering mathematics
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Call number:SPRINGER-2010-9780387729237:ONLINE Show nearby items on shelf
Title:Discrete Integrable Systems [electronic resource] : QRT Maps and Elliptic Surfaces
Author(s): J.J Duistermaat
Date:2010
Edition:1
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The rich subject matter in this book brings in mathematics from different domains, especially from the theory of elliptic surfaces and dynamics.The material comes from the authors insights and understanding of a birationaltransformation of the plane derived from a discrete sine-Gordon equation, posing the question of determining the behavior of the discrete dynamical system defined by the iterates of the map. The aim of this book is to give a completetreatment not only of the basic facts about QRT ma ps, but also the background theory on which these maps are based. Readers with a good knowledge of algebraic geometry will be interested in Kodairas theory of elliptic surfaces andthe collection of nontrivial applications presented here. While prerequisit es for some readers will demand their knowledge of quite a bit of algebraic- and complex analytic geometry, different categories of readers will be able tobecome familiar with any selected interest in the book without having to make an extensive journey t hrough the literature
Note:Springer eBooks
Contents:The QRT Map
The Pencil of Biquadratic Curves in
The QRT surface
Cubic Curves in the Projective Plane
The Action of the QRT Map on Homology
Elliptic Surfaces
Automorphisms of Elliptic Surfaces
Elliptic Fibrations with a Real Structure
Rational elliptic surfaces
Symmetric QRT Maps
Examples from the Literature
Appendices
ISBN:9780387729237
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382 : v304
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Functions of complex variables , Number theory
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Call number:SPRINGER-2010-9780387709147:ONLINE Show nearby items on shelf
Title:Functional Analysis, Sobolev Spaces and Partial Differential Equations [electronic resource]
Author(s): Haim Brezis
Date:2010
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Uniquely, this book presents a coherent, concise and unified way of combining elements from two distinct worlds, functional analysis (FA) and partial differential equations (PDEs), and is intended for students who have agood background in real analys is. This text presents a smooth transition from FA to PDEs by analyzing in great detail the simple case of one-dimensional PDEs (i.e., ODEs), a more manageable approach for the beginner. Although there aremany books on functional analysis and many on PDEs , this is the first to cover both of these closely connected topics. Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research.This book has its roots in a celebrated course taught by the author for many years and is a completely revised, updated, and expanded English edition of the important Analyse Fonctionnelle (1983). Since the French book was firstpublished, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chin ese. The English version is a welcome addition to this list. The first part of the text deals with abstract results in FA and operatortheory. The second part is concerned with the study of spaces of functions (of one or more real variables) having specifi c differentiability properties, e.g., the celebrated Sobolev spaces, which lie at the heart of the modern theoryof PDEs. The Sobolev spaces occur in a wide range of questions, both in pure and applied mathematics, appearing in linear and nonlinear PDEs wh ich arise, for example, in differential geometry, harmonic analysis, engineering, mechanics,physics etc. and belong in the toolbox of any graduate student studying analysis
Note:Springer eBooks
Contents:Preface
1. The HahnBanach Theorems. Introduction to the Theory of Conjugate Convex Functions
2. The Uniform Boundedness Principle and the Closed Graph Theorem. Unbounded Operators. Adjoint. Characterization of Surjective Operators
3. Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity
4. L^p Spaces
5. Hilbert Spaces
6. Compact Operators. Spectral Decomposition of Self
Adjoint Compact Operators
7. The HilleYosida Theorem
8. Sobolev Spaces and the Variational Formulation of Boundary Value Problems in One Dimension
9. Sobolev Spaces and the Vari
ISBN:9780387709147
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Differential equations, partial
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Call number:SPRINGER-2009-9783642001734:ONLINE Show nearby items on shelf
Title:Mathematics for Physicists and Engineers [electronic resource] : Fundamentals and Interactive Study Guide
Author(s): Klaus Weltner
Wolfgang J Weber
Jean Grosjean
Peter Schuster
Date:2009
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Mathematics is the basic language in physics and engineering. It is an essential tool which first and second year students have to master as soon as possible. A lack of competence in mathematics is the main reason for failure anddrop out in the begin ning periods of study. This textbook offers an accessible and highly approved approach which is characterized by the combination of the textbook with a detailed study guide available online at extras.springer.com.This study guide divides the whole learnin g task into small units which the student is very likely to master successfully. Thus he or she is asked to read and study a limited section of the textbook and to return to the study guideafterwards. Working with the study guide his or her learning resul ts are controlled, monitored and deepened by graded questions, exercises, repetitions and finally by problems and applications of the content studied. Since the degreeof difficulties is slowly rising the students gain confidence and experience their own p rogress in mathematical competence thus fostering motivation. Furthermore in case of learning difficulties he or she is given supplementaryexplanations and in case of individual needs supplementary exercises and applications. So the sequence of the studie s is individualised according to the individual performance and needs and can be regarded as full tutorial course. Morethan that the study guide aims to satisfy two objectives simultaneously: firstly it enables students to make effective use of the textbo ok and secondly it offers advice on the improvement of study skills. Empirical studies have shownthat the student's competence for using written information has improved significantly by using this study guide
Note:Springer eBooks
Contents:Vector Algebra I: Scalars and Vectors
Vector Algebra II: Scalar and Vector Products
Functions
Exponential, Logarithmic and Hyperbolic Functions
Differential Calculus
Integral Calculus
Applications of Integration
Taylor Series and Power Series
Complex Numbers
Differential Equations
Laplace Transforms
Functions of Several Variables Partial Differentiation and Total Differentiation
Multiple Integrals Coordinate Systems
Transformation of Coordinates Matrices
Sets of Linear Equations Determinants
Eigenvalues and Eigenvectors of Real Matrices
Vect
ISBN:9783642001734
Series:e-books
Series:SpringerLink (Online service)
Series:Physics and Astronomy (Springer-11651)
Keywords: Mathematical physics , Engineering mathematics
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Call number:SPRINGER-2009-9783034600040:ONLINE Show nearby items on shelf
Title:Applied Pseudoanalytic Function Theory [electronic resource]
Author(s): Vladislav V Kravchenko
Date:2009
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Pseudoanalytic function theory generalizes and preserves many crucial features of complex analytic function theory. The Cauchy-Riemann system is replaced by a much more general first-order system with variable coefficients whichturns out to be closel y related to important equations of mathematical physics. This relation supplies powerful tools for studying and solving Schrdinger, Dirac, Maxwell, Klein-Gordon and other equations with the aid ofcomplex-analytic methods. The book is dedicated to these r ecent developments in pseudoanalytic function theory and their applications as well as to multidimensional generalizations. It is directed to undergraduates, graduate studentsand researchers interested in complex-analytic methods, solution techniques for equations of mathematical physics, partial and ordinary differential equations
Note:Springer eBooks
Contents:Pseudoanalytic Function Theory and Second
order Elliptic Equations
Definitions and Results from Bers Theory
Solutions of Second
order Elliptic Equations as Real Components of Complex Pseudoanalytic Functions
Formal Powers
Cauchys Integral Formula
Complex Riccati Equation
Applications to Sturm
Liouville Theory
A Representation for Solutions of the Sturm
Liouville Equation
Spectral Problems and Darboux Transformation
Applications to Real First
order Systems
Beltrami Fields
Static Maxwell System in Axially Symmetric Inhomogeneous Media
Hyperbolic Pseudoan
ISBN:9783034600040
Series:e-books
Series:SpringerLink (Online service)
Series:Frontiers in Mathematics, 1660-8046
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables , Operator theory , Differential equations, partial , Mathematical physics
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Call number:SPRINGER-2009-9781441905499:ONLINE Show nearby items on shelf
Title:Cauchys Cours danalyse [electronic resource] : An Annotated Translation
Author(s): Robert E Bradley
C. Edward Sandifer
Date:2009
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
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Note:This is an annotated and indexed translation (from French into English) of Augustin Louis Cauchy's 1821 classic textbook Cours d'analyse. This is the first English translation of a landmark work in mathematics, one of the mostinfluential texts in the history of mathematics. It belongs in every mathematics library, along with Newton's Principia and Euclid's Elements. The authors' style mimics the look and feel of the second French edition. It is anessentially modern textbook style, about 75% narrative and 25% theorems, proofs, corollaries. Despite the extensive narrative, it has an essentially Euclidean architecture in its careful ordering of definitions and theorems. It wasthe first book in analysis to do this. Cauchy's book is essentially a precalcu lus book, with a rigorous exposition of the topics necessary to learn calculus. Hence, any good quality calculus student can understand the content of thevolume. The basic audience is anyone interested in the history of mathematics, especially 19th centur y analysis. In addition to being an important book, the Cours d'analyse is well-written, packed with unexpected gems, and, in general,a thrill to read. Robert E. Bradley is Professor of Mathematics at Adelphi University. C. Edward Sandifer is Professor of Mathematics at Western Connecticut State University
Note:Springer eBooks
Contents:Translators Introduction
Cauchy's Introduction
Preliminaries
First Part: Algebraic Analysis
On Real Functions
On Quantities that are Infinitely Small or Infinitely Large, and on the Continuity of Functions
On Symmetric Functions and Alternating Functions
Determination of Integer Functions
Determination of continuous functions of a single variable that satisfy certain conditions
On convergent and divergent (real) series
On imaginary expressions and their moduli
On imaginary functions and variables
On convergent and divergent imaginary series
On real or
ISBN:9781441905499
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 , Global analysis (Mathematics) , Mathematics_$xHistory
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Call number:SPRINGER-2009-9780817646561:ONLINE Show nearby items on shelf
Title:Integration and Modern Analysis [electronic resource]
Author(s): John J Benedetto
Wojciech Czaja
Date:2009
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:A paean to twentieth century analysis, this modern text has several important themes and key features which set it apart from others on the subject. A major thread throughout is the unifying influence of the concept of absolutecontinuity on different iation and integration. This leads to fundamental results such as the DieudonnGrothendieck theorem and other intricate developments dealing with weak convergence of measures. Key Features: * Fascinatinghistorical commentary interwoven into the exposition * Hundreds of problems from routine to challenging * Broad mathematical perspectives and material, e.g., in harmonic analysis and probability theory, for independent studyprojects * Two significant appendices on functional analysis and Fourier analysis. K ey Topics: * In-depth development of measure theory and Lebesgue integration * Comprehensive treatment of connection between differentiation andintegration, as well as complete proofs of state-of-the-art results * Classical real variables and introduction to the role of Cantor sets, later placed in the modern setting of self-similarity and fractals * Evolution of the Rieszrepresentation theorem to Radon measures and distribution theory * Deep results in modern differentiation theory * Systematic developme nt of weak sequential convergence inspired by theorems of Vitali, Nikodym, and HahnSaks *Thorough treatment of rearrangements and maximal functions * The relation between surface measure and Hausforff measure * Complete presentation of Besicovich covering s and differentiation of measures. Integration and Modern Analysiswill serve advanced undergraduates and graduate students, as well as professional mathematicians. It may be used in the classroom or self-study
Note:Springer eBooks
Contents:Preface
Classical real variables
Lebesgue measure and general measure theory
The Lebesgue integral
The relationship between differentiation and integration on R
Spaces of measures and the RadonNikodym theorem
Weak convergence of measures
Riesz representation theorem
Lebesgue differentiation theorem on Rd
Self
similar sets and fractals
Appendix I: Functional analysis
Appendix II: Fourier Analysis
References
Index
ISBN:9780817646561
Series:e-books
Series:SpringerLink (Online service)
Series:Birkhuser Advanced Texts / Basler Lehrbcher
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functions of complex variables
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Call number:SPRINGER-2009-9780387094342:ONLINE Show nearby items on shelf
Title:Modern Fourier Analysis [electronic resource]
Author(s): Loukas Grafakos
Date:2009
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The primary goal of these two volumes is to present the theoretical foundation of the field of Euclidean Harmonic analysis. The original edition was published as a single volume, but due to its size, scope, and the addition ofnew material, the second edition consists of two volumes. The present edition contains a new chapter on time-frequency analysis and the Carleson-Hunt theorem. The first volume contains the classical topics such as Interpolation,Fourier Series, the Fourier Transform, Maximal Func tions, Singular Integrals, and Littlewood-Paley Theory. The second volume contains more recent topics such as Function Spaces, Atomic Decompositions, Singular Integrals ofNonconvolution Type, and Weighted Inequalities. These volumes are mainly addressed t o graduate students in mathematics and are designed for a two-course sequence on the subject with additional material included for reference. Theprerequisites for the first volume are satisfactory completion of courses in real and complex variables. The s econd volume assumes material from the first. This book is intended to present the selected topics in depth and stimulatefurther study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of a nalysis on the torus. This material is included for historical reasons, as the genesis of Fourieranalysis can be found in trigonometric expansions of periodic functions in several variables. About the first edition: Grafakos's book is very user-friendly w ith numerous examples illustrating the definitions and ideas... Thetreatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises. - Kenneth Ross, MAA Online
Note:Springer eBooks
Contents:Smoothness and Function Spaces
and Carleson Measures
Singular Integrals of Nonconvolution Type
Weighted Inequalities
Boundedness and Convergence of Fourier Integrals
Time Frequency Analysis and the CarlesonHunt Theorem
ISBN:9780387094342
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v250
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Harmonic analysis , Fourier analysis , Functional analysis
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Call number:SPRINGER-2009-9780387094328:ONLINE Show nearby items on shelf
Title:Classical Fourier Analysis [electronic resource]
Author(s): Loukas Grafakos
Date:2009
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The primary goal of these two volumes is to present the theoretical foundation of the field of Euclidean Harmonic analysis. The original edition was published as a single volume, but due to its size, scope, and the addition ofnew material, the second edition consists of two volumes. The present edition contains a new chapter on time-frequency analysis and the Carleson-Hunt theorem. The first volume contains the classical topics such as Interpolation,Fourier Series, the Fourier Transform, Maximal Func tions, Singular Integrals, and Littlewood-Paley Theory. The second volume contains more recent topics such as Function Spaces, Atomic Decompositions, Singular Integrals ofNonconvolution Type, and Weighted Inequalities. These volumes are mainly addressed t o graduate students in mathematics and are designed for a two-course sequence on the subject with additional material included for reference. Theprerequisites for the first volume are satisfactory completion of courses in real and complex variables. The s econd volume assumes material from the first. This book is intended to present the selected topics in depth and stimulatefurther study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of a nalysis on the torus. This material is included for historical reasons, as the genesis of Fourieranalysis can be found in trigonometric expansions of periodic functions in several variables. About the first edition: Grafakos's book is very user-friendly w ith numerous examples illustrating the definitions and ideas... Thetreatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises. - Kenneth Ross, MAA Online
Note:Springer eBooks
Contents:Preface
Lp Spaces and Interpolation
Maximal Functions, Fourier Transform, and Distributions
Fourier Analysis on the Torus
Singular Integrals of Convolution Type
Littlewood
Paley Theory and Multipliers
Gamma and Beta Functions
Bessel Functions
Rademacher Functions
Spherical Coordinates
Some Trigonometric Identities and Inequalities
Summation by Parts
Basic Functional Analysis
The Minimax Lemma
The Schur Lemma
The Whitney Decomposition of Open Sets in Rn
Smoothness and Vanishing Moments
Glossary
References
Index
ISBN:9780387094328
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v249
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Harmonic analysis , Fourier analysis , Functional analysis
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Call number:SPRINGER-2008-9783764382728:ONLINE Show nearby items on shelf
Title:Holomorphic Functions in the Plane and n-dimensional Space [electronic resource]
Author(s): Klaus Grlebeck
Klaus Habetha
Wolfgang Sprig
Date:2008
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-calledquaternionic and Clifford or h ypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensionalresults based on a uniform notion of holomorphy. Hi storical remarks, lots of examples, figures and exercises accompany each chapter
Note:Springer eBooks
Contents:Introduction
I. Numbers
Complex Numbers
Quaternions
Clifford numbers
II. Functions
Topological Aspects
Holomorphic Functions
Power Functions and Mbius Transformations
III. Integration und Integral Theorems
Integral Theorems and
formulas
Teodorescu Transformation
IV. Series and Local Properties
Power Series
Orthogonal Series
Elementary Functions
Local Structure of Holomorphic Functions
Special Functions
Appendices
Bibliography
Index
ISBN:9783764382728
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functions of complex variables , Integral Transforms , Potential theory (Mathematics)
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Call number:SPRINGER-2008-9780817647032:ONLINE Show nearby items on shelf
Title:Shape-Preserving Approximation by Real and Complex Polynomials [electronic resource]
Author(s): Sorin G Gal
Date:2008
Publisher:Boston, MA : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This monograph presents the first comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables. Such approximation methods are useful in many problems thatarise in science and engin eering and require an optimal mathematical representation of physical reality. The main topics are structured in four chapters, followed by an appendix: shape-preserving approximation and interpolation of realfunctions of one real variable by real polynom ials shape-preserving approximation of real functions of several real variables by multivariate real polynomials shape-preserving approximation of analytic functions of one complexvariable by complex polynomials in the unit disk and shape-preserving appro ximation of analytic functions of several complex variables on the unit ball or the unit polydisk by polynomials of several complex variables. The appendixtreats related results of non-polynomial and non-spline approximations preserving shape including th ose by complexified operators with applications to complex partial differential equations. Shape-Preserving Approximation by Real andComplex Polynomials contains many open problems at the end of each chapter to stimulate future research along with a rich and updated bibliography surveying the vast literature. The text will be useful to graduate students andresearchers interested in approximation theory, mathematical analysis, numerical analysis, computer aided geometric design, robotics, data fitting, che mistry, fluid mechanics, and engineering
Note:Springer eBooks
Contents:Preface
Shape Preserving Approximation by Real Univariate Polynomials
Shape Preserving Approximation by Real Multivariate Polynomials
Shape Preserving Approximation by Complex Univariate Polynomials
Shape Preserving Approximation by Complex Multivariate Polynomials
Appendix: Some Related Topics
References
Index
ISBN:9780817647032
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Functions of complex variables , Computer science Mathematics , Engineering mathematics
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Call number:SPRINGER-2007-9783764377786:ONLINE Show nearby items on shelf
Title:Wavelet Analysis and Applications [electronic resource]
Author(s): Tao Qian
Mang I Vai
Yuesheng Xu
Date:2007
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume reflects the latest developments in the area of wavelet analysis and its applications. Since the cornerstone lecture of Yves Meyer presented at the ICM 1990 in Kyoto, to some extent, wavelet analysis has often beensaid to be mainly an app lied area. However, a significant percentage of contributions now are connected to theoretical mathematical areas, and the concept of wavelets continuously stretches across various disciplines of mathematics.Key topics: Approximation and Fourier Analysis Construction of Wavelets and Frame Theory Fractal and Multifractal Theory Wavelets in Numerical Analysis Time-Frequency Analysis Adaptive Representation of Nonlinear and Non-stationarySignals Applications, particularly in image processing Through the broa d spectrum, ranging from pure and applied mathematics to real applications, the book will be most useful for researchers, engineers and developers alike
Note:Springer eBooks
Contents:Preface
I. Wavelet Theory
1. Approximation and Fourier Analysis
2. Construction of Wavelets and Frame Theory
3. Fractal and Multifractal Theory, Wavelet Algorithms, Wavelets in Numerical Analysis
4. Time
Frequency Analysis, Adaptive Representation of Nonlinear and Non
stationary Signals
II. Wavelet Applications
ISBN:9783764377786
Series:e-books
Series:SpringerLink (Online service)
Series:Applied and Numerical Harmonic Analysis
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Harmonic analysis , Fourier analysis , Functions of complex variables , Operator theory , Numerical analysis
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Call number:SPRINGER-2007-9783540695745:ONLINE Show nearby items on shelf
Title:Sharp Real-Part Theorems [electronic resource] : A Unified Approach
Author(s): Vladimir Maz'ya
Gershon Kresin
Date:2007
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume contains a coherent point of view on various sharp pointwise inequalities for analytic functions in a disk in terms of the real part of the function on the boundary circle or in the disk itself. Inequalities of thistype are frequently use d in the theory of entire functions and in the analytic number theory. Rich opportunities are anticipated to extend these inequalities to analytic functions of several complex variables and solutions of partialdifferential equations
Note:Springer eBooks
Contents:Preface
Introduction
Estimates for analytic functions bounded with respect to their real part
Estimates for analytic functions with respect to the Lp
norm of Re f on the circle
Estimates for analytic functions by the best Lp
approximation of Re f on the circle
Estimates for directional derivatives of harmonic functions
Estimates for derivatives of analytic functions
Bohr's type real part estimates
Estimates for the increment of derivatives of analytic functions
References
Index
List of symbols
ISBN:9783540695745
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v1903
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables , Potential theory (Mathematics)
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Call number:SPRINGER-2007-9783540326915:ONLINE Show nearby items on shelf
Title:Statistical Methods for Biostatistics and Related Fields [electronic resource]
Author(s): Wolfgang Hrdle
Yuichi Mori
Philippe Vieu
Date:2007
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Biostatistics is one of the scientific fields for which the recent developments have been extremely important. It is also strongly related to other scientific disciplines involving statistical methodology. The aim of this book isto cover a wide scope of recent statistical methods used by scientists in biostatistics as well as in other related fields such as chemometrics, environmetrics and geophysics. The contributed papers, coming from internationallyrecognized researchers, present various statistic al methodologies together with a selected scope of their main mathematical properties and their applications in real case studies, making this book of interest to a wide audience amongresearchers and students in statistics. Each method is accompanied with interactive and automatic Xplore routines, available on-line, allowing people to reproduce the proposed examples or to apply the methods to their own realdatasets. Thus this book will also be of special interest to practitioners
Note:Springer eBooks
Contents:Biostatistics
Discriminant Analysis Based on Continuous and Discrete Variables
Longitudinal Data Analysis with Linear Regression
A Kernel Method Used for the Analysis of Replicated Micro
array Experiments
Kernel Estimates of Hazard Functions for Biomedical Data Sets
Partially Linear Models
Analysis of Contingency Tables
Identifying Coexpressed Genes
Bootstrap Methods for Testing Interactions in GAMs
Survival Trees
A Semiparametric Approach to Estimate Reference Curves for Biophysical Properties of the Skin
Survival Analysis
Related Sciences
Ozone Pollutio
ISBN:9783540326915
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Statistics , Mathematical statistics
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Call number:SPRINGER-2007-9780817645380:ONLINE Show nearby items on shelf
Title:Polynomial Convexity [electronic resource]
Author(s): Edgar Lee Stout
Date:2007
Publisher:Boston, MA : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This comprehensive monograph is devoted to the study of polynomially convex sets, which play an important role in the theory of functions of several complex variables. Important features of Polynomial Convexity: *Presents thegeneral properties of pol ynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets. *Motivates the theory with numerous examples and counterexamples, which serve to illustrate the general theoryand to delineate its boundaries. *Examines in considerable detail questions of uniform approximation, especially on totally real sets, for the most part on compact sets but with some attention to questions of global approximation onnoncompact sets. *Discusses important applications, e.g., to the stu dy of analytic varieties and to the theory of removable singularities for CR functions. *Requires of the reader a solid background in real and complex analysistogether with some previous experience with the theory of functions of several complex variables as well as the elements of functional analysis. This beautiful exposition of a rich and complex theory, which contains much material notavailable in other texts, is destined to be the standard reference for many years, and will appeal to all those with a n interest in multivariate complex analysis
Note:Springer eBooks
Contents:From the contents Preface
Introduction
Some General Properties of Polynomially Convex Sets
Sets of Finite Length
Sets of Class A1
Further Results
Approximation
Varieties in Strictly
Pseudoconvex Domains
Examples and Counter Examples
Bibliography
Index
ISBN:9780817645380
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v261
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Field theory (Physics) , Global analysis (Mathematics) , Functional analysis , Functions of complex variables , Differential equations, partial
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Call number:SPRINGER-2007-9780387497631:ONLINE Show nearby items on shelf
Title:Bounded Analytic Functions [electronic resource]
Author(s): John B Garnett
Date:2007
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The book, which covers a wide range of beautiful topics in analysis, is extremely well organized and well written, with elegant, detailed proofs. The book has educated a whole generation of mathematicians with backgrounds incomplex analysis and funct ion algebras. It has had a great impact on the early careers of many leading analysts and has been widely adopted as a textbook for graduate courses and learning seminars in both the US and abroad. - From theCitation for the 2003 Leroy P. Steele Prize for Exposition The author has not attempted to produce a compendium. Rather, he has selected a range of topics in a many-faceted theory and, within that range, penetrated to considerabledepth...the author has succeeded in bringing out the beauty of a theory which, despite its relatively advanced age---now approaching 80 years---continues to surprise and to delight its practitioners. The author has left his mark on thesubject. - Donald Sarason, Mathematical Reviews Garnett's Bounded Analytic Functions is to f unction theory as Zygmund's Trigonometric Series is to Fourier analysis. Bounded Analytic Functions is widely regarded as a classic textbookused around the world to educate today's practioners in the field, and is the primary source for the experts. It is beautifully written, but intentionally cannot be read as a novel. Rather it gives just the right level of detail sothat the motivated student develops the requisite skills of the trade in the process of discovering the beauty of the combination of real, complex and functional analysis. - Donald E. Marshall, University of Washington
Note:Springer eBooks
Contents:Preliminaries
H_P Spaces
Conjugate Functions
Some Extremal Problems
Some Uniform Algebra
Bounded Mean Oscillation
Interpolating Sequences
The Corona Construction
Douglas Algebras
Interpolating Sequences and Maximal Ideals
Bibliography
Index
ISBN:9780387497631
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v236
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Functions of complex variables
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Call number:SPRINGER-2006-9783764376055:ONLINE Show nearby items on shelf
Title:Shift-invariant Uniform Algebras on Groups [electronic resource]
Author(s): Suren A Grigoryan
Thomas V Tonev
Date:2006
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The central subject of the book - the theory of shift-invariant algebras - is an outgrowth of the established theory of generalized analytic functions. Associated subalgebras of almost periodic functions of real variables and ofbounded analytic funct ions on the unit disc are carried along within the general framework. In particular, it is shown that the algebra of almost periodic functions with spectrum in a semigroup of the reals does not have ahalf-plane-corona if and only if all non-negative semic haracters of the semigroup are monotone decreasing, or equivalently, if and only if the strong hull of the semigroup coincides with the positive half of its group envelope. Underthe same conditions the corresponding subalgebra of bounded analytic function s on the disc has neither a half-plane-corona nor a disc-corona. There are given characterizations of semigroups such that classical theorems of complexanalysis hold on the associated shift-invariant algebras. Bourgain algebras, orthogonal measures, and p rimary ideals of big disc algebras are described. The notion of a harmonic function is extended on compact abelian groups, andcorresponding Fatou-type theorems are proven. Important classes of inductive limits of standard uniform algebras, including Blasc he algebras, are introduced and studied. In particular, it is shown that algebras of hyper-analyticfunctions, associated with families of inner functions, do not have a big-disc-corona
Note:Springer eBooks
Contents:Preface
1. Banach Algebras and Uniform Algebras
2. Three Classical Families of Functions
3. Groups and Semigroups
4. Shift
invariant Algebras on Compact Groups
5. Extension of Semicharacters and Additive Weights
6. G
disc Algebras
7. Harmonicity on Groups and G
discs
8. Shift
invariant Algebras and Inductive Limit Algebras on Groups
Bibliography
Index
ISBN:9783764376055
Series:e-books
Series:SpringerLink (Online service)
Series:Monografie Matematyczne, Instytut Matematyczny Polskiel Akademii Nauk (IMPAN) : v68
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Functions of complex variables , Operator theory
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Call number:SPRINGER-2006-9783764375454:ONLINE Show nearby items on shelf
Title:The Fourfold Way In Real Analysis [electronic resource] An Alternative to the Metaplectic Representation
Author(s): Andr Unterberger
Date:2006
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The fourfold way starts with the consideration of entire functions of one variable satisfying specific estimates at infinity, both on the real line and the pure imaginary line. A major part of classical analysis, mainly that whichdeals with Fourier a nalysis and related concepts, can then be given a parameter-dependent analogue. The parameter is some real number modulo 2, the classical case being obtained when it is an integer. The space L2(R) has to give way toa pseudo-Hilbert space, on which a new t ranslation-invariant integral still exists. All this extends to the n-dimensional case, and in the alternative to the metaplectic representation so obtained, it is the space of Lagrangiansubspaces of R2n that plays the usual role of the complex Siegel dom ain. In fourfold analysis, the spectrum of the harmonic oscillator can be an arbitrary class modulo the integers. Even though the whole development touches uponnotions of representation theory, pseudodifferential operator theory, and algebraic geometry, i t remains completely elementary in all these aspects. The book should be of interest to researchers working in analysis in general, inharmonic analysis, or in mathematical physics
Note:Springer eBooks
Contents:The One
dimensional Anaplectic Representation
The n
dimensional Anaplectic Analysis
Towards the Anaplectic Symbolic Calculi
The One
dimensional Case Revisited
ISBN:9783764375454
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v250
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Harmonic analysis , Functions of complex variables , Mathematical physics
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Call number:SPRINGER-2006-9783764373955:ONLINE Show nearby items on shelf
Title:On the Topology of Isolated Singularities in Analytic Spaces [electronic resource]
Author(s): Jos Seade
Date:2006
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostlydevoted to complex sing ularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor the relation with3-dimensional Lie groups exotic spheres spin st ructures and 3-manifold invariants the geometry of quadrics and Arnold's theorem which states that the complex projective plane modulo conjugation is the 4-sphere. The second part ofthe book studies pioneer work about real analytic singularities which ari se from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred linksin the 3-sphere defined by meromorphic functions. This provides new methods for constructing m anifolds equipped with a rich geometry. The book is largely self-contained and serves a wide audience of graduate students, mathematiciansand researchers interested in geometry and topology
Note:Springer eBooks
Contents:Preface
Introduction
A Fast Trip through the Classical Theory
Motions in Plane Geometry and the 3
Dimensional Brieskorn Manifolds
3
Dimensional Lie Groups and Surface Singularities
Within the Realm of the General Index Theorem
On the Geometry and Topology of Quadrics in CP^n
Real Singularities and Complex Geometry
Real Singularities with a Milnor Fibration
Real Singularities and Open Book Decompositions of the 3
Sphere
Bibliography
Index
ISBN:9783764373955
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v241
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Functions of complex variables , Global differential geometry , Algebraic topology
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Call number:SPRINGER-2006-9780817645137:ONLINE Show nearby items on shelf
Title:Complex Variables with Applications [electronic resource]
Author(s): S Ponnusamy
Herb Silverman
Date:2006
Publisher:Boston, MA : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector. Examined properly, each perspective provides crucial insight into the interrelations between thecomplex number system a nd its parent, the real number system. The authors explore these relationships by adopting both generalization and specialization methods to move from real variables to complex variables, and vice versa, whilesimultaneously examining their analytic and ge ometric characteristics, using geometry to illustrate analytic concepts and employing analysis to unravel geometric notions. The engaging exposition is replete with discussions, remarks,questions, and exercises, motivating not only understanding on the pa rt of the reader, but also developing the tools needed to think critically about mathematical problems. This focus involves a careful examination of the methods andassumptions underlying various alternative routes that lead to the same destination. The ma terial includes numerous examples and applications relevant to engineering students, along with some techniques to evaluate various types ofintegrals. The book may serve as a text for an undergraduate course in complex variables designed for scientists an d engineers or for mathematics majors interested in further pursuing the general theory of complex analysis. The onlyprerequisite is a basic knowledge of advanced calculus. The presentation is also ideally suited for self-study
Note:Springer eBooks
Contents:Algebraic and Geometric Preliminaries
Topological and Analytic Preliminaries
Bilinear Transformations and Mappings
Elementary Functions
Analytic Functions
Power Series
Complex Integration and Cauchys Theorem
Applications of Cauchys Theorem
Laurent Series and the Residue Theorem
Harmonic Functions
Conformal Mapping and the Riemann Mapping Theorem
Entire and Meromorphic Functions
Analytic Continuation
ISBN:9780817645137
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables , Differential equations, partial , Geometry , Number theory , Engineering mathematics
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Call number:SPRINGER-2006-9780817644406:ONLINE Show nearby items on shelf
Title:Geometric Function Theory [electronic resource] : Explorations in Complex Analysis
Author(s): Steven G Krantz
Date:2006
Publisher:Boston, MA : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research,including invariant ge ometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphicfunctions, the inhomogeneous CauchyRiemann equations, and the corona problem. The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, the topics are presented with anunderstanding and explanation of their interrelations with other im portant parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory.Although the book examines complex analysis from many different points of view, it uses geomet ric analysis as its unifying theme. This methodically designed book contains a rich collection of exercises, examples, and illustrationswithin each individual chapter, concluding with an extensive bibliography of monographs, research papers, and a thoroug h index. Seeking to capture the imagination of advanced undergraduate and graduate students with a basic backgroundin complex analysisand also to spark the interest of seasoned workers in the fieldthe book imparts a solid education both in complex analysi s and in how modern mathematics works
Note:Springer eBooks
Contents:Classical Function Theory
Invariant Geometry
Variations on the Theme of the Schwarz Lemma
Normal Families
The Riemann Mapping Theorem and Its Generalizations
Boundary Regularity of Conformal Maps
The Boundary Behavior of Holomorphic Functions
Real and Harmonic Analysis
The Cauchy
Riemann Equations
The Greens Function and the Poisson Kernel
Harmonic Measure
Conjugate Functions and the Hilbert Transform
Wolffs Proof of the Corona Theorem
Algebraic Topics
Automorphism Groups of Domains in the Plane
Cousin Problems, Cohomology, and Sheaves
ISBN:9780817644406
Series:e-books
Series:SpringerLink (Online service)
Series:Cornerstones
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Harmonic analysis , Functions of complex variables , Differential equations, partial , Potential theory (Mathematics) , Global differential geometry
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Call number:SPRINGER-2006-9780387245362:ONLINE Show nearby items on shelf
Title:Real and Complex Clifford Analysis [electronic resource]
Author(s): Sha Huang
Yu Ying Qiao
Guo Chun Wen
Date:2006
Publisher:Boston, MA : Springer US
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Clifford analysis, a branch of mathematics that has been developed since about 1970, has important theoretical value and several applications. In this book, the authors introduce many properties of regular functions andgeneralized regular functions i n real Clifford analysis, as well as harmonic functions in complex Clifford analysis. It covers important developments in handling the incommutativity of multiplication in Clifford algebra, thedefinitions and computations of high-order singular integrals, boundary value problems, and so on. In addition, the book considers harmonic analysis and boundary value problems in four kinds of characteristic fields proposed by LuogengHua for complex analysis of several variables. The great majority of the contents originate in the authors investigations, and this new monograph will be interesting for researchers studying the theory of functions. Audience Thisbook is intended for mathematicians studying function theory
Note:Springer eBooks
Contents:General Regular and Harmonic Functions in Real and Complex Clifford Analysis
Boundary Value Problems of Generalized Regular Functions and Hyperbolic Harmonic Functions in Real Clifford Analysis
Nonlinear Boundary Value Problems for Generalized Biregular Functions in Real Clifford Analysis
Boundary Value Problems of Second Order Partial Differential Equations for Classical Domains in Real Clifford Analysis
Integrals Dependent on Parameters and Singular Integral Equations in Real Clifford Analysis
Several Kinds of High Order Singular Integrals and Differential Integral Equations i
ISBN:9780387245362
Series:e-books
Series:SpringerLink (Online service)
Series:Advances in Complex Analysis and Its Applications : v5
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Integral equations , Differential equations, partial
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Call number:SPRINGER-2005-9780817644413:ONLINE Show nearby items on shelf
Title:Basic Real Analysis [electronic resource] : Along with a companion volume Advanced Real Analysis
Author(s): Anthony W Knapp
Date:2005
Publisher:Boston, MA : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiringor established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features of Basic Real Analysis: *Early chapters treat the fundamentals of real variables, sequences and series of functions, the theory of Fourier series for the Riemann integral, metric spaces, and the theoretical underpinnings of multivariable calculus anddifferential equations * Subsequent chapters develop the Lebesgue theory in Euclidean and abstract spaces, Fourier series and the Fourier transform for the Lebesgue integral, point-set topology, measure theory in locally compactHausdorff spaces, and the basics of Hilbert and Banach spaces * The subjects of Fourier series and harm onic functions are used as recurring motivation for a number of theoretical developments * The development proceeds from theparticular to the general, often introducing examples well before a theory that incorporates them * The text includes many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most ofthe problems Basic Real Analysis requires of the reader only familiarity with some linear algebra and real variable theory, the very beginning of group theory, and an acquaintance with proofs. It is suitable as a text in an advancedundergraduate course in real variable theory and in most basic graduate courses in Lebesgue integration and related topics. Because it focuses on what every young mathematicia n needs to know about real analysis, the book is ideal bothas a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal
Note:Springer eBooks
Contents:Theory of Calculus in One Real Variable
Metric Spaces
Theory of Calculus in Several Real Variables
Theory of Ordinary Differential Equations and Systems
Lebesgue Measure and Abstract Measure Theory
Measure Theory for Euclidean Space
Differentiation of Lebesgue Integrals on the Line
Fourier Transform in Euclidean Space
Lp Spaces
Topological Spaces
Integration on Locally Compact Spaces
Hilbert and Banach Spaces
ISBN:9780817644413
Series:e-books
Series:SpringerLink (Online service)
Series:Cornerstones
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Fourier analysis , Differential Equations , Topology
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Call number:SPRINGER-2004-9783662077313:ONLINE Show nearby items on shelf
Title:Hardy Operators, Function Spaces and Embeddings
Author(s): David E Edmunds
Date:2004
Size:1 online resource (328 p.)
Note:10.1007/978-3-662-07731-3
Contents:1 Preliminaries -- 2 Hardy-type Operators -- 3 Banach function spaces -- 4 Poincaré and Hardy inequalities -- 5 Generalised ridged domains -- 6 Approximation numbers of Sobolev embeddings -- References -- Author Index -- Notation
Index
ISBN:9783662077313
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Functional analysis , Integral equations , Operator theory , Differential equations , Partial differential equations , Functions of real variables , Mathematics , Functional Analysis , Real Functions , Ordinary Differential Equations , Partial Differential Equations , Integral Equations , Operator Theory
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Call number:SPRINGER-2004-9783662058008:ONLINE Show nearby items on shelf
Title:Applied Mathematics: Body and Soul Calculus in Several Dimensions
Author(s): Kenneth Eriksson
Date:2004
Size:1 online resource (426 p.)
Note:10.1007/978-3-662-05800-8
Contents:54. Vector-Valued Functions of Several Real Variables -- 55. Level Curves/Surfaces and the Gradient -- 56. Linearization and Stability of Initial Value Problems -- 57. Adaptive Solvers of Initial Value Problems -- 58. Lorenz and the
Essence of Chaos -- 59. Optimization -- 60. The Divergence, Rotation and Laplacian -- 61. Meteorology and Coriolis Forces -- 62. Curve Integrals -- 63. Double Integrals -- 64. Surface Integrals -- 65. Multiple Integrals -- 66. Gauss'
Theorem and Green's Formula in R2 -- 67. Gauss' Theorem and Green's Formula in R3 -- 68. Stokes' Theorem -- 69. Potential Fields -- 70. Center of Mass and Archimedes' Principle -- 71. Newton's Nightmare -- 72. Laplacian Models -- 73.
Chemical Reactions -- 74. Calculus Tool Bag II -- 75. Piecewise Linears in R2 and R3 -- 76. FEM for Boundary Value Problems in R2 and R3 -- 77. Inverse Problems -- 78. Differential Equations Tool Bag -- 79. Applications Tool Bag -- 80.
Analytic Functions -- 81. Fourier Series -- 82. Fourier Transforms -- 83. Incompressible Navier-Stokes: Quick and Easy -- 84. Fourier Analysis Tool Bag -- 85. Analytic Functions Tool Bag II -- Index
ISBN:9783662058008
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Chemometrics , Matrix theory , Algebra , Mathematical analysis , Analysis (Mathematics) , Computer mathematics , Physics , Applied mathematics , Engineering mathematics , Mathematics , Analysis , Linear and Multilinear Algebras, Matrix Theory , Computational Mathematics and Numerical Analysis , Math. Applications in Chemistry , Appl.Mathematics/Computational Methods of Engineering , Mathematical Methods in Physics
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