Functional Analysis
An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras
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Beschreibung
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 single variable assumed of the reader.
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.
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
Autor*in
Joseph Muscat
Themen in »Functional Analysis«
Banach Algebra Banach Space Metric Space Hilbert Space Spectral theory C*-algebra Textbook on Functional Analysis
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“This is a book for the bookshelf! It covers a wide range of important theory, the exposition is clear, there are barely any typos, and one gets this nice feeling that the author knows what he is talking about and has an honest wish that the reader should learn and understand.” (Olav Nygaard, zbMATH 1546.46001, 2024)
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