Functional Analysis

An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras

Nonfiction, Science & Nature, Mathematics, Functional Analysis
Cover of the book Functional Analysis by Joseph Muscat, Springer International Publishing
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Author: Joseph Muscat ISBN: 9783319067285
Publisher: Springer International Publishing Publication: July 23, 2014
Imprint: Springer Language: English
Author: Joseph Muscat
ISBN: 9783319067285
Publisher: Springer International Publishing
Publication: July 23, 2014
Imprint: Springer
Language: English

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.

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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.

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