Classical and Discrete Functional Analysis with Measure Theory

ISBN-13: 9781107634886 / Angielski / Miękka / 2022 / 350 str.

Martin Buntinas

Opis

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

Recenzje

'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)

Spis treści

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.