Charles W Swartz's Books

Functional Calculi

By: Charles W Swartz,Carlos Bosch

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A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function space into a subspace of continuous linear operators, i.e. a method for defining “functions of an operator”. Perhaps the most familiar example is based on the spectral theorem for bounded self-adjoint operators on a complex Hilbert space.This book contains an exposition of several such functional calculi. In particular, there is an exposition based on the spectral theorem for bounded, self-adjoint operators, an extension to the case of several commuting self-adjoint operators and an extension to normal operators. The Riesz operational calculus based on the Cauchy integral theorem from complex analysis is also described. Finally, an exposition of a functional calculus due to H. Weyl is given.

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226

Publisher

World Scientific

Published Date

ISBN 10

9814415995

ISBN 13

9789814415996

Infinite Matrices And The Gliding Hump, Matrix Methods In Analysis

By: Charles W Swartz

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Infinite Matrices And The Gliding Hump, Matrix Methods In Analysis

By: Charles W Swartz

These notes present a theorem on infinite matrices with values in a topological group due to P Antosik and J Mikusinski. Using the matrix theorem and classical gliding hump techniques, a number of applications to various topics in functional analysis, measure theory and sequence spaces are given. There are a number of generalizations of the classical Uniform Boundedness Principle given; in particular, using stronger notions of sequential convergence and boundedness due to Antosik and Mikusinski, versions of the Uniform Boundedness Principle and the Banach-Steinhaus Theorem are given which, in contrast to the usual versions, require no completeness or barrelledness assumptions on the domain space. Versions of Nikodym Boundedness and Convergence Theorems of measure theory, the Orlicz-Pettis Theorem on subseries convergence, generalizations of the Schur Lemma on the equivalence of weak and norm convergence in l1 and the Mazur-Orlicz Theorem on the continuity of separately continuous bilinear mappings are also given. Finally, the matrix theorems are also employed to treat a number of topics in sequence spaces.

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222

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World Scientific

Published Date

ISBN 10

9814498718

ISBN 13

9789814498715

Measure, Integration And Function Spaces

By: Charles W Swartz

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Measure, Integration And Function Spaces

By: Charles W Swartz

This text contains a basic introduction to the abstract measure theory and the Lebesgue integral. Most of the standard topics in the measure and integration theory are discussed. In addition, topics on the Hewitt-Yosida decomposition, the Nikodym and Vitali-Hahn-Saks theorems and material on finitely additive set functions not contained in standard texts are explored. There is an introductory section on functional analysis, including the three basic principles, which is used to discuss many of the classic Banach spaces of functions and their duals. There is also a chapter on Hilbert space and the Fourier transform.

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294

Publisher

World Scientific

Published Date

ISBN 10

9814502510

ISBN 13

9789814502511

Introduction To Gauge Integrals

By: Charles W Swartz

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Introduction To Gauge Integrals

By: Charles W Swartz

This book presents the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. These variations lead to integrals which are much more powerful than the Riemann integral. The Henstock/Kurzweil integral is an unconditional integral for which the fundamental theorem of calculus holds in full generality, while the McShane integral is equivalent to the Lebesgue integral in Euclidean spaces.A basic knowledge of introductory real analysis is required of the reader, who should be familiar with the fundamental properties of the real numbers, convergence, series, differentiation, continuity, etc.

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Page Count

169

Publisher

World Scientific

Published Date

ISBN 10

9814493511

ISBN 13

9789814493512

Theories Of Integration: The Integrals Of Riemann, Lebesgue, Henstock-kurzweil, And Mcshane

By: Charles W Swartz,Douglas S Kurtz

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Theories Of Integration: The Integrals Of Riemann, Lebesgue, Henstock-kurzweil, And Mcshane

By: Charles W Swartz,Douglas S Kurtz

This book presents a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil, and McShane, showing how new theories of integration were developed to solve problems that earlier theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and can be used separately in teaching a portion of an introductory course on real analysis. There is a sufficient supply of exercises to make the book useful as a textbook.

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Page Count

283

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813106336

ISBN 13

9789813106338

Elementary Functional Analysis

By: Charles W Swartz

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Elementary Functional Analysis

By: Charles W Swartz

This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators.

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192

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813107529

ISBN 13

9789813107526

Abstract Duality Pairs In Analysis

By: Charles W Swartz

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Abstract Duality Pairs In Analysis

By: Charles W Swartz

The book presents a theory of abstract duality pairs which arises by replacing the scalar field by an Abelian topological group in the theory of dual pair of vector spaces. Examples of abstract duality pairs are vector valued series, spaces of vector valued measures, spaces of vector valued integrable functions, spaces of linear operators and vector valued sequence spaces. These examples give rise to numerous applications such as abstract versions of the Orlicz-Pettis Theorem on subseries convergent series, the Uniform Boundedness Principle, the Banach-Steinhaus Theorem, the Nikodym Convergence theorems and the Vitali-Hahn-Saks Theorem from measure theory and the Hahn-Schur Theorem from summability. There are no books on the current market which cover the material in this book. Readers will find interesting functional analysis and the many applications to various topics in real analysis.

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Page Count

302

Publisher

World Scientific

Published Date

ISBN 10

9813232781

ISBN 13

9789813232785

Elements of Real Analysis

By: Charles G. Denlinger

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Elements of Real Analysis

By: Charles G. Denlinger

Elementary Real Analysis is a core course in nearly all mathematics departments throughout the world. It enables students to develop a deep understanding of the key concepts of calculus from a mature perspective. Elements of Real Analysis is a student-friendly guide to learning all the important ideas of elementary real analysis, based on the author's many years of experience teaching the subject to typical undergraduate mathematics majors. It avoids the compact style of professional mathematics writing, in favor of a style that feels more comfortable to students encountering the subject for the first time. It presents topics in ways that are most easily understood, yet does not sacrifice rigor or coverage. In using this book, students discover that real analysis is completely deducible from the axioms of the real number system. They learn the powerful techniques of limits of sequences as the primary entry to the concepts of analysis, and see the ubiquitous role sequences play in virtually all later topics. They become comfortable with topological ideas, and see how these concepts help unify the subject. Students encounter many interesting examples, including "pathological" ones, that motivate the subject and help fix the concepts. They develop a unified understanding of limits, continuity, differentiability, Riemann integrability, and infinite series of numbers and functions.

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Page Count

769

Publisher

Jones & Bartlett Publishers

Published Date

ISBN 10

1449659934

ISBN 13

9781449659936

Elements of Real Analysis

By: Charles Denlinger

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Elements of Real Analysis

By: Charles Denlinger

A student-friendly guide to learning all the important ideas of elementary real analysis, this resource is based on the author's many years of experience teaching the subject to typical undergraduate mathematics majors.

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769

Publisher

Jones & Bartlett Learning

Published Date

ISBN 10

0763779474

ISBN 13

9780763779474

Theories Of Integration: The Integrals Of Riemann, Lebesgue, Henstock-kurzweil, And Mcshane (2nd Edition)

By: Charles W Swartz,Douglas S Kurtz

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Theories Of Integration: The Integrals Of Riemann, Lebesgue, Henstock-kurzweil, And Mcshane (2nd Edition)

By: Charles W Swartz,Douglas S Kurtz

The book uses classical problems to motivate a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil and McShane, showing how new theories of integration were developed to solve problems that earlier integration theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and could be used separately in teaching a portion of an introductory real analysis course. There is a sufficient supply of exercises to make this book useful as a textbook.

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Page Count

311

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813108266

ISBN 13

9789813108264

Book's by Charles W Swartz

Functional Calculi

Functional Calculi

Infinite Matrices And The Gliding Hump, Matrix Methods In Analysis

Infinite Matrices And The Gliding Hump, Matrix Methods In Analysis

Measure, Integration And Function Spaces

Measure, Integration And Function Spaces

Introduction To Gauge Integrals

Introduction To Gauge Integrals

Theories Of Integration: The Integrals Of Riemann, Lebesgue, Henstock-kurzweil, And Mcshane

Theories Of Integration: The Integrals Of Riemann, Lebesgue, Henstock-kurzweil, And Mcshane

Elementary Functional Analysis

Elementary Functional Analysis

Abstract Duality Pairs In Analysis

Abstract Duality Pairs In Analysis

Elements of Real Analysis

Elements of Real Analysis

Elements of Real Analysis

Elements of Real Analysis

Theories Of Integration: The Integrals Of Riemann, Lebesgue, Henstock-kurzweil, And Mcshane (2nd Edition)

Theories Of Integration: The Integrals Of Riemann, Lebesgue, Henstock-kurzweil, And Mcshane (2nd Edition)

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