Functional Analysis: An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras

This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields.

Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.

1119058286
Functional Analysis: An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras

This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields.

Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.

69.99 In Stock
Functional Analysis: An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras

Functional Analysis: An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras

by Joseph Muscat
Functional Analysis: An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras
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Functional Analysis: An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras

Functional Analysis: An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras

by Joseph Muscat

Overview

This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields.

Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.

Product Details

ISBN-13: 9783319067285
Publisher: Springer-Verlag New York, LLC
Publication date: 07/23/2014
Sold by: Barnes & Noble
Format: eBook
File size: 21 MB
Note: This product may take a few minutes to download.

About the Author

Professor Joseph Muscat graduated from the University of Oxford and obtained his Ph.D. from Princeton University with a thesis on the Maxwell–Klein–Gordon equation on curved space-time. He has written several papers on the applications of functional analysis to inverse problems in the biomedical field and is a co-author of the novel ACSP method in EEG signal processing.

Table of Contents

1 Introduction.- Part I: Metric Spaces.- 2 Distance.- 3 Convergence and Continuity.- 4 Completeness and Separability.- 5 Connectedness.- 6 Compactness.- Part II: Banach and Hilbert Spaces.- 7 Normed Spaces.- 8 Continuous Linear Maps.- 9 The Classical Spaces.- 10 Hilbert Spaces.- 11 Banach Spaces.- 12 Differentiation and Integration.- Part III: Banach Algebras.- 13 Banach Algebras.- 14 Spectral Theory.- 15 C*-Algebras.
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Mathematical Analysis - Functional Analysis
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Mathematics
Mathematical Analysis
Mathematical Analysis - Functional Analysis

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