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. 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.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.
|Title||:||Probabilistic Techniques in Analysis|
|Author||:||Richard F. Bass|
|Publisher||:||Springer Science & Business Media - 1995|