Overview
- Provides a self-contained introduction to functional analysis, assuming only real analysis and linear algebra
- Presents the essential aspects of metric spaces, Hilbert spaces, Banach spaces and Banach algebras
- Includes interesting applications of Hilbert spaces such as least squares approximation and inverse problems
- Prepares the reader for graduate-level mathematical analysis
- Includes supplementary material: sn.pub/extras
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Table of contents (15 chapters)
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Front Matter
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Metric Spaces
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Front Matter
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Banach and Hilbert Spaces
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Front Matter
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Banach Algebras
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Functional Analysis
Book Subtitle: An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras
Authors: Joseph Muscat
DOI: https://doi.org/10.1007/978-3-319-06728-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2014
eBook ISBN: 978-3-319-06728-5Published: 23 July 2014
Edition Number: 1
Number of Pages: XI, 420
Number of Illustrations: 75 b/w illustrations
Topics: Functional Analysis, Operator Theory