Overview
- Includes over 1000 examples and exercises
- Contains interesting applications such as least squares approximation, inverse problems, and SVD
- Assumes only single-variable real analysis and linear algebra
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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 provides an introduction to functional analysis suitable for lecture courses to final year undergraduates or beginning graduates.
Starting from the very basics of metric spaces, the book adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, including the spectral theorem, the Gelfand transform, and Banach algebras. Various applications, such as least squares approximation, inverse problems, and Tikhonov regularization, illustrate the theory. Over 1000 worked examples and exercises of varying difficulty present the reader with ample material for reflection.
This new edition of Functional Analysis has been completely revised and corrected, with many passages rewritten for clarity, numerous arguments simplified, and a good amount of new material added, including new examples and exercises. The prerequisites, however, remain the same with only knowledge of linear algebra and real analysis of a singlevariable assumed of the reader.
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/10.1007/978-3-031-27537-1
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 2024
Softcover ISBN: 978-3-031-27536-4Published: 29 February 2024
eBook ISBN: 978-3-031-27537-1Published: 28 February 2024
Edition Number: 2
Number of Pages: XIII, 464
Number of Illustrations: 71 b/w illustrations, 1 illustrations in colour
Topics: Functional Analysis, Operator Theory