Probabilistic techniques in analysis
By: Bass, Richard F.
Series: Probability and its applications: a series of the applied probability trust. / edited by J. Gani.Publisher: New York Springer-Verlag 1995Description: xii, 392p.ISBN: 9780387943879.Subject(s): Mathematical analysis | ProbabilitiesDDC classification: 515 | B293p Summary: In recent years, there has been an upsurge of interest in using techniques drawn from probability to tackle problems in analysis. These applications arise in subjects such as potential theory, harmonic analysis, singular integrals, and the study of analytic functions. This book presents a modern survey of these methods at the level of a beginning Ph.D. student. Highlights of this book include the construction of the Martin boundary, probabilistic proofs of the boundary Harnack principle, Dahlberg's theorem, a probabilistic proof of Riesz' theorem on the Hilbert transform, and Makarov's theorems on the support of harmonic measure. The author assumes that a reader has some background in basic real analysis, but the book includes proofs of all the results from probability theory and advanced analysis required. Each chapter concludes with exercises ranging from the routine to the difficult. In addition, there are included discussions of open problems and further avenues of research.| Item type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
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Books
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PK Kelkar Library, IIT Kanpur | General Stacks | 515 B293p (Browse shelf) | Available | A184091 |
Browsing PK Kelkar Library, IIT Kanpur Shelves , Collection code: General Stacks Close shelf browser
| 515 At55t3 Theoretical numerical analysis | 515 AT56T THEORETICAL NUMERICAL ANALYSIS | 515 At56t2 Theoretical numerical analysis | 515 B293p Probabilistic techniques in analysis | 515 B455t A tour of the calculus | 515 B456M MATHEMATICAL ANALYSIS | 515 B456P A PROBLEM BOOK IN MATHEMATICAL ANALYSIS |
In recent years, there has been an upsurge of interest in using techniques drawn from probability to tackle problems in analysis. These applications arise in subjects such as potential theory, harmonic analysis, singular integrals, and the study of analytic functions. This book presents a modern survey of these methods at the level of a beginning Ph.D. student. Highlights of this book include the construction of the Martin boundary, probabilistic proofs of the boundary Harnack principle, Dahlberg's theorem, a probabilistic proof of Riesz' theorem on the Hilbert transform, and Makarov's theorems on the support of harmonic measure. The author assumes that a reader has some background in basic real analysis, but the book includes proofs of all the results from probability theory and advanced analysis required. Each chapter concludes with exercises ranging from the routine to the difficult. In addition, there are included discussions of open problems and further avenues of research.
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