Classical and Discrete Functional Analysis with Measure Theory

Martin Buntinas

350 pages, parution le 19/01/2022

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Résumé

This book concentrates on discrete aspects of functional analysis, including Fourier series, sequence spaces, and matrix maps. It is suitable for advanced undergraduates and above, and is an excellent textbook for capstone courses in mathematical analysis as well as beginning graduate courses in measure theory and functional analysis.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.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.

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Martin Buntinas
Parution	19/01/2022
Nb. de pages	350
EAN13	9781107634886

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Classical and Discrete Functional Analysis with Measure Theory

Résumé

Caractéristiques techniques

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