Classical and Discrete Functional Analysis with Measure Theory

This advanced undergraduate/beginning graduate text covers measure theory and discrete aspects of functional analysis, with 760 exercises.

Martin Buntinas (Author)

9781107634886, Cambridge University Press

Paperback / softback, published 20 January 2022

350 pages
23 x 15.2 x 2.8 cm, 0.72 kg

'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)

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.

Subject Areas: Functional analysis & transforms [PBKF]