[PDF/ePub] An Introductory Course In Lebesgue Spaces Cms Books In Mathematics Download Book

An Introductory Course in Lebesgue Spaces

Posted on 2016-06-23 by Rene Erlin Castillo,Humberto Rafeiro

Author: Rene Erlin Castillo,Humberto Rafeiro

Publisher: Springer

ISBN: 3319300342

Category: Mathematics

Page: 461

This book is devoted exclusively to Lebesgue spaces and their direct derived spaces. Unique in its sole dedication, this book explores Lebesgue spaces, distribution functions and nonincreasing rearrangement. Moreover, it also deals with weak, Lorentz and the more recent variable exponent and grand Lebesgue spaces with considerable detail to the proofs. The book also touches on basic harmonic analysis in the aforementioned spaces. An appendix is given at the end of the book giving it a self-contained character. This work is ideal for teachers, graduate students and researchers.

Functional Analysis

Posted on 2016-12-19 by Gerardo Chacón,Humberto Rafeiro,Juan Camilo Vallejo

A Terse Introduction

Author: Gerardo Chacón,Humberto Rafeiro,Juan Camilo Vallejo

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110441926

Category: Mathematics

Page: 245

This textbook on functional analysis offers a short and concise introduction to the subject. The book is designed in such a way as to provide a smooth transition between elementary and advanced topics and its modular structure allows for an easy assimilation of the content. Starting from a dedicated chapter on the axiom of choice, subsequent chapters cover Hilbert spaces, linear operators, functionals and duality, Fourier series, Fourier transform, the fixed point theorem, Baire categories, the uniform bounded principle, the open mapping theorem, the closed graph theorem, the Hahn–Banach theorem, adjoint operators, weak topologies and reflexivity, operators in Hilbert spaces, spectral theory of operators in Hilbert spaces, and compactness. Each chapter ends with workable problems. The book is suitable for graduate students, but also for advanced undergraduates, in mathematics and physics. Contents: List of Figures Basic Notation Choice Principles Hilbert Spaces Completeness, Completion and Dimension Linear Operators Functionals and Dual Spaces Fourier Series Fourier Transform Fixed Point Theorem Baire Category Theorem Uniform Boundedness Principle Open Mapping Theorem Closed Graph Theorem Hahn–Banach Theorem The Adjoint Operator Weak Topologies and Reflexivity Operators in Hilbert Spaces Spectral Theory of Operators on Hilbert Spaces Compactness Bibliography Index

An Illustrative Introduction to Modern Analysis

Posted on 2018-01-02 by Nikolaos Katzourakis,Eugen Varvaruca

Author: Nikolaos Katzourakis,Eugen Varvaruca

Publisher: CRC Press

ISBN: 1351765329

Category: Mathematics

Page: 558

Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis. The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.

Analysis

Posted on 2016-12-18 by Jean-Paul Penot

From Concepts to Applications

Author: Jean-Paul Penot

Publisher: Springer

ISBN: 331932411X

Category: Mathematics

Page: 669

This textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results that can be applied to concrete problems. In addition to classical results of functional analysis, differential calculus and integration, Analysis discusses topics such as convex analysis, dissipative operators and semigroups which are often absent from classical treatises. Acknowledging that analysis has significantly contributed to the understanding and development of the present world, the book further elaborates on techniques which pervade modern civilization, including wavelets in information theory, the Radon transform in medical imaging and partial differential equations in various mechanical and physical phenomena. Advanced undergraduate and graduate students, engineers as well as practitioners wishing to familiarise themselves with concepts and applications of analysis will find this book useful. With its content split into several topics of interest, the book’s style and layout make it suitable for use in several courses, while its self-contained character makes it appropriate for self-study.

An Introduction to Modern Analysis

Posted on 2015-05-04 by Vicente Montesinos,Peter Zizler,Václav Zizler

Author: Vicente Montesinos,Peter Zizler,Václav Zizler

Publisher: Springer

ISBN: 3319124811

Category: Mathematics

Page: 863

Examining the basic principles in real analysis and their applications, this text provides a self-contained resource for graduate and advanced undergraduate courses. It contains independent chapters aimed at various fields of application, enhanced by highly advanced graphics and results explained and supplemented with practical and theoretical exercises. The presentation of the book is meant to provide natural connections to classical fields of applications such as Fourier analysis or statistics. However, the book also covers modern areas of research, including new and seminal results in the area of functional analysis.

Best Approximation in Inner Product Spaces

Posted on 2012-12-06 by Frank R. Deutsch

Author: Frank R. Deutsch

Publisher: Springer Science & Business Media

ISBN: 1468492985

Category: Mathematics

Page: 338

This is the first systematic study of best approximation theory in inner product spaces and, in particular, in Hilbert space. Geometric considerations play a prominent role in developing and understanding the theory. The only prerequisites for reading the book is some knowledge of advanced calculus and linear algebra.

An Introduction to Modern Analysis

Posted on 2015-05-04 by Vicente Montesinos,Peter Zizler,Václav Zizler

Author: Vicente Montesinos,Peter Zizler,Václav Zizler

Publisher: Springer

ISBN: 3319124811

Category: Mathematics

Page: 863

Examining the basic principles in real analysis and their applications, this text provides a self-contained resource for graduate and advanced undergraduate courses. It contains independent chapters aimed at various fields of application, enhanced by highly advanced graphics and results explained and supplemented with practical and theoretical exercises. The presentation of the book is meant to provide natural connections to classical fields of applications such as Fourier analysis or statistics. However, the book also covers modern areas of research, including new and seminal results in the area of functional analysis.

Newsletter

Posted on 2000 by New Zealand Mathematical Society

Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

Fourier Analysis

Posted on 2011-10-07 by Eric Stade

Author: Eric Stade

Publisher: John Wiley & Sons

ISBN: 1118165519

Category: Mathematics

Page: 520

A reader-friendly, systematic introduction to Fourier analysis Rich in both theory and application, Fourier Analysis presents a unique and thorough approach to a key topic in advanced calculus. This pioneering resource tells the full story of Fourier analysis, including its history and its impact on the development of modern mathematical analysis, and also discusses essential concepts and today's applications. Written at a rigorous level, yet in an engaging style that does not dilute the material, Fourier Analysis brings two profound aspects of the discipline to the forefront: the wealth of applications of Fourier analysis in the natural sciences and the enormous impact Fourier analysis has had on the development of mathematics as a whole. Systematic and comprehensive, the book: Presents material using a cause-and-effect approach, illustrating where ideas originated and what necessitated them Includes material on wavelets, Lebesgue integration, L2 spaces, and related concepts Conveys information in a lucid, readable style, inspiring further reading and research on the subject Provides exercises at the end of each section, as well as illustrations and worked examples throughout the text Based upon the principle that theory and practice are fundamentally linked, Fourier Analysis is the ideal text and reference for students in mathematics, engineering, and physics, as well as scientists and technicians in a broad range of disciplines who use Fourier analysis in real-world situations.

Principles of Mathematical Analysis

Posted on 1976 by Walter Rudin

Author: Walter Rudin

Publisher: McGraw-Hill Publishing Company

ISBN: 9780070856134

Category: Mathematics

Page: 342

The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Convex Functions and their Applications

Posted on 2006-02-11 by Constantin Niculescu,Lars-Erik Persson

A Contemporary Approach

Author: Constantin Niculescu,Lars-Erik Persson

Publisher: Springer Science & Business Media

ISBN: 0387310770

Category: Mathematics

Page: 256

Thorough introduction to an important area of mathematics Contains recent results Includes many exercises

Two Millennia of Mathematics

Posted on 2012-12-06 by George M. Phillips

From Archimedes to Gauss

Author: George M. Phillips

Publisher: Springer Science & Business Media

ISBN: 1461211808

Category: Mathematics

Page: 223

A collection of inter-connected topics in areas of mathematics which particularly interest the author, ranging over the two millennia from the work of Archimedes to the "Werke" of Gauss. The book is intended for those who love mathematics, including undergraduate students of mathematics, more experienced students and the vast unseen host of amateur mathematicians. It is equally a useful source of material for those who teach mathematics.

Lectures on Functional Analysis and the Lebesgue Integral

Posted on 2016-06-03 by Vilmos Komornik

Author: Vilmos Komornik

Publisher: Springer

ISBN: 1447168119

Category: Mathematics

Page: 403

This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This approach leads naturally to the basic notions and theorems. Most results are illustrated by the small lp spaces. The Lebesgue integral, meanwhile, is treated via the direct approach of Frigyes Riesz, whose constructive definition of measurable functions leads to optimal, clear-cut versions of the classical theorems of Fubini-Tonelli and Radon-Nikodým. Lectures on Functional Analysis and the Lebesgue Integral presents the most important topics for students, with short, elegant proofs. The exposition style follows the Hungarian mathematical tradition of Paul Erdős and others. The order of the first two parts, functional analysis and the Lebesgue integral, may be reversed. In the third and final part they are combined to study various spaces of continuous and integrable functions. Several beautiful, but almost forgotten, classical theorems are also included. Both undergraduate and graduate students in pure and applied mathematics, physics and engineering will find this textbook useful. Only basic topological notions and results are used and various simple but pertinent examples and exercises illustrate the usefulness and optimality of most theorems. Many of these examples are new or difficult to localize in the literature, and the original sources of most notions and results are indicated to help the reader understand the genesis and development of the field.

Variable Lebesgue Spaces

Posted on 2013-02-12 by David Cruz-Uribe,Alberto Fiorenza

Foundations and Harmonic Analysis

Author: David Cruz-Uribe,Alberto Fiorenza

Publisher: Springer Science & Business Media

ISBN: 3034805489

Category: Mathematics

Page: 312

This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.

Martingales in Banach Spaces

Posted on 2016-06-06 by Gilles Pisier

Author: Gilles Pisier

Publisher: Cambridge University Press

ISBN: 1316679462

Category: Mathematics

Page: N.A

This book focuses on the major applications of martingales to the geometry of Banach spaces, and a substantial discussion of harmonic analysis in Banach space valued Hardy spaces is also presented. It covers exciting links between super-reflexivity and some metric spaces related to computer science, as well as an outline of the recently developed theory of non-commutative martingales, which has natural connections with quantum physics and quantum information theory. Requiring few prerequisites and providing fully detailed proofs for the main results, this self-contained study is accessible to graduate students with a basic knowledge of real and complex analysis and functional analysis. Chapters can be read independently, with each building from the introductory notes, and the diversity of topics included also means this book can serve as the basis for a variety of graduate courses.

Explorations in Harmonic Analysis

Posted on 2009-05-24 by Steven G. Krantz

With Applications to Complex Function Theory and the Heisenberg Group

Author: Steven G. Krantz

Publisher: Springer Science & Business Media

ISBN: 9780817646691

Category: Mathematics

Page: 362

This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.

Generalized Inverses

Posted on 2006-04-18 by Adi Ben-Israel,Thomas N.E. Greville

Theory and Applications

Author: Adi Ben-Israel,Thomas N.E. Greville

Publisher: Springer Science & Business Media

ISBN: 0387216340

Category: Mathematics

Page: 420

This second edition accounts for many major developments in generalized inverses while maintaining the informal and leisurely style of the 1974 first edition. Added material includes a chapter on applications, new exercises, and an appendix on the work of E.H. Moore.

Harmonic and Complex Analysis in Several Variables

Posted on 2017-09-20 by Steven G. Krantz

Author: Steven G. Krantz

Publisher: Springer

ISBN: 3319632310

Category: Mathematics

Page: 424

Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.

Functional Analysis and Infinite-Dimensional Geometry

Posted on 2013-04-17 by Marian Fabian,Petr Habala,Petr Hajek,Vicente Montesinos Santalucia,Jan Pelant,Vaclav Zizler

Author: Marian Fabian,Petr Habala,Petr Hajek,Vicente Montesinos Santalucia,Jan Pelant,Vaclav Zizler

Publisher: Springer Science & Business Media

ISBN: 1475734808

Category: Mathematics

Page: 451

This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints.

The History of Approximation Theory

Posted on 2007-07-28 by Karl-Georg Steffens

From Euler to Bernstein

Author: Karl-Georg Steffens

Publisher: Springer Science & Business Media

ISBN: 9780817644758

Category: Mathematics

Page: 219

* Exciting exposition integrates history, philosophy, and mathematics * Combines a mathematical analysis of approximation theory with an engaging discussion of the differing philosophical underpinnings behind its development * Appendices containing biographical data on numerous eminent mathematicians, explanations of Russian nomenclature and academic degrees, and an excellent index round out the presentation