書誌事項

Harmonic analysis

Barry Simon

(A comprehensive course in analysis, pt. 3)

American Mathematical Society, c2015

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注記

Includes bibliographical references and indexes

内容説明・目次

内容説明

A Comprehensive Course in Analysis by Poincare Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 3 returns to the themes of Part 1 by discussing pointwise limits (going beyond the usual focus on the Hardy-Littlewood maximal function by including ergodic theorems and martingale convergence), harmonic functions and potential theory, frames and wavelets, $H^p$ spaces (including bounded mean oscillation (BMO)) and, in the final chapter, lots of inequalities, including Sobolev spaces, Calderon-Zygmund estimates, and hypercontractive semigroups.

目次

Preliminaries Pointwise convergence almost everywhere Harmonic and subharmonic functions Bonus chapter: Phase space analysis $H^p$ spaces and boundary values of analytic functions on the unit disk Bonus chapter: More inequalities Bibliography Symbol index Subject index Author index Index of capsule biographies

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