Classical and Discrete Functional Analysis with Measure Theory
Published on 26. January 2022
978-1-009-23433-7 (ISBN)
Description
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.
Reviews / Votes
'Every theorem, proposition, lemma, and corollary has a very understandable proof, is easy to follow, and is well supported by the previous results (in the sense of a self-contained book). ... I do not hesitate to say that this book is not far from being an encyclopedic book in functional analysis-measure theory-Fourier series.' Rigoberto Vera Mendoza, MathSciNet (https://mathscinet.ams.org)More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Illustrations
Worked examples or Exercises
File size
4,39 MB
ISBN-13
978-1-009-23433-7 (9781009234337)
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Schweitzer Classification
Other editions
Additional editions
Martin Buntinas
Classical and Discrete Functional Analysis with Measure Theory
Book
01/2022
Cambridge University Press
€151.50
Shipment within 15-20 days
Person
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.
Content
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.
