Classical and discrete functional analysis with measure theory / Martin Buntinas.

Format:

Book

Author/Creator:

Buntinas, Martin, author.

Series:

London Mathematical Society student texts ; 101.

London Mathematical Society student texts ; 101

Language:

English

Subjects (All):

Functional analysis.

Measure theory.

Physical Description:

1 online resource (xi, 458 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2022.

Summary:

Functional analysis deals with infinite-dimensional spaces. Its results are among the greatest achievements of modern mathematics and it has wide-reaching applications to probability theory, statistics, economics, classical and quantum physics, chemistry, engineering, and pure mathematics. This book deals with measure theory and discrete aspects of functional analysis, including Fourier series, sequence spaces, matrix maps, and summability. Based on the author's extensive teaching experience, the text is accessible to advanced undergraduate and first-year graduate students. It can be used as a basis for a one-term course or for a one-year sequence, and is suitable for self-study for readers with an undergraduate-level understanding of real analysis and linear algebra. More than 750 exercises are included to help the reader test their understanding. Key background material is summarized in the Preliminaries.

Contents:

Lebesgue measure

Lebesgue integral

Some calculus

Abstract measures

Metric and normed spaces

Linear operators

Fourier series

Applications

Sequence spaces

Matrix maps, multipliers, and duality

Summability.

Notes:

Title from publisher's bibliographic system (viewed on 10 Jan 2022).

Other Format:

Print version:

ISBN:

9781139524445 (ebook)

Access Restriction:

Restricted for use by site license.