000			01647 a2200229 4500
005			20181217135905.0
008			181212b xxu||||| |||| 00| 0 eng d
020			_a9780387943879
040			_cIIT Kanpur
041			_aeng
082			_a515 _bB293p
100			_aBass, Richard F.
245			_aProbabilistic techniques in analysis _cRichard F. Bass
260			_bSpringer-Verlag _c1995 _aNew York
300			_axii, 392p.
440			_aProbability and its applications: a series of the applied probability trust
490			_a/ edited by J. Gani
520			_aIn 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.
650			_aMathematical analysis
650			_aProbabilities
942			_cBK
999			_c559538 _d559538