Buntinas M. Classical and Discrete Functional Analysis with Measure Theory

Cambridge: Cambridge University Press, 2022. — 470 p.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.FrontmatterPreliminaries
Measure And Integration
Lebesgue Measure
Lebesgue Integral
Some Calculus
Abstract Measures
Elements Of Classical Functional Analysis
Metric and Normed Spaces
Linear Operators
Discrete Functional Analysis
Fourier Series
Applications
Sequence Spaces
Matrix Maps Multipliers and Duality
Summability