Probabilistic Techniques in Analysis (Hardcover)

Richard F. Bass

ISBN 10: 0387943870 / ISBN 13: 9780387943879

Published by Springer-Verlag New York Inc., New York, NY, 1994

About this Item

Hardcover. 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 PhD student. Highlights include the construction of the Martin boundary, probabilistic proofs of the boundary Harnack principle, Dahlberg's theorem, a probabilistic proof of Riesz's theorem on the Hilbert transform, and Makarov's theorems on the support of harmonic measure. The author assumes that the reader has some background in basic real analysis, but the book includes proofs of all results from probability theory and advanced analysis required. Each chapter concludes with exercises ranging from the routine to the difficult. In addition, there are discussions of open problems and further avenues of research. Highlights 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. This book includes proofs of the results from probability theory and advanced analysis required. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9780387943879

Bibliographic Details

• Title: Probabilistic Techniques in Analysis (Hardcover)
• Publisher: Springer-Verlag New York Inc., New York, NY
• Publication Date: 1994
• Language: English
• ISBN 10: 0387943870
• ISBN 13: 9780387943879
• Binding: Hardcover
• Condition: new

About this title

Synopsis

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.

From the Back Cover

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.