Classical and Discrete Functional Analysis with Measure Theory

Martin Buntinas (Loyola University, Chicago)

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English

Cambridge University Press
20 January 2022

Functional analysis & transforms

Series: London Mathematical Society Student Texts

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.

By: Martin Buntinas (Loyola University Chicago)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: New edition
Dimensions: Height: 235mm, Width: 158mm, Spine: 34mm
Weight: 860g
ISBN: 9781107034143
ISBN 10: 1107034140
Series: London Mathematical Society Student Texts
Pages: 350
Publication Date: 20 January 2022
Audience: General/trade , ELT Advanced
Format: Hardback
Publisher's Status: Active

Preliminaries; Part I. Measure and Integration: 1. Lebesgue measure; 2. Lebesgue integral; 3. Some calculus; 4. Abstract measures; Part II. Elements of Classical Functional Analysis: 5. Metric and normed spaces; 6. Linear operators; Part III. Discrete Functional Analysis: 7. Fourier series; 8. Applications; 9. Sequence spaces; 10. Matrix maps, multipliers, and duality; 11. Summability; Index.

Martin Buntinas is Professor Emeritus in the Department of Mathematics and Statistics at Loyola University Chicago, where he served as the chair of the Department of Mathematical & Computer Sciences from 1992 to 1998. He publishes in the areas of functional analysis, sequence spaces, Fourier series, and approximation theory. He has been a Humboldt and a Fulbright Senior Scholar, and has organized numerous international conferences in sequence spaces.