Harmonic Analysis
A Comprehensive Course in Analysis, Part 3
Seiten
2015
American Mathematical Society (Verlag)
978-1-4704-1102-2 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-1102-2 (ISBN)
A Comprehensive Course in Analysis by 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. Part 3 returns to the themes of Part 1 by discussing pointwise limits, harmonic functions and potential theory, frames and wavelets, $H^p$ spaces and inequalities.
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.
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.
Barry Simon, California Institute of Technology, Pasadena, CA, USA.
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
Erscheinungsdatum | 15.01.2016 |
---|---|
Verlagsort | Providence |
Sprache | englisch |
Maße | 178 x 254 mm |
Gewicht | 500 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
Mathematik / Informatik ► Mathematik ► Analysis | |
ISBN-10 | 1-4704-1102-4 / 1470411024 |
ISBN-13 | 978-1-4704-1102-2 / 9781470411022 |
Zustand | Neuware |
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