Probabilistic Techniques in Analysis: PROBABILISTIC TECHNIQUES IN AN

Hardcover | December 16, 1994

byRichard F. BassEditorJ. Gani, T. Kurtz

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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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From Our Editors

A glance at almost any probability book shows that there has been a large flow of ideas from analysis to probability theory. This book is concerned with the flow of ideas in the opposite direction. The topics covered are those branches of analysis to which probability has contributed something, in new results, new proofs, or new insigh...

From the Publisher

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 ...

Format:HardcoverDimensions:420 pages, 9.21 × 6.14 × 0 inPublished:December 16, 1994Publisher:Springer New York

The following ISBNs are associated with this title:

ISBN - 10:0387943870

ISBN - 13:9780387943879

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From Our Editors

A glance at almost any probability book shows that there has been a large flow of ideas from analysis to probability theory. This book is concerned with the flow of ideas in the opposite direction. The topics covered are those branches of analysis to which probability has contributed something, in new results, new proofs, or new insights.