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Gaussian Harmonic Analysis
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Gaussian Harmonic Analysis

2019 ed.

by Wilfredo Urbina-Romero

Book Details

Format Hardback or Cased Book
Book Series Springer Monographs in Mathematics
ISBN-10 3030055965
ISBN-13 9783030055967
Edition 2019 ed.
Publisher Springer Nature Switzerland AG
Imprint Springer Nature Switzerland AG
Country of Manufacture GB
Country of Publication GB
Publication Date Jul 4th, 2019
Print length 477 Pages
Product Classification: Complex analysis, complex variables
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Authored by a ranking authority in Gaussian harmonic analysis, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: harmonic analysis and probability.

Authored by a ranking authority in Gaussian harmonic analysis, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: harmonic analysis and  probability. The book is intended for a very diverse audience, from graduate students all the way to researchers working in a broad spectrum of areas in analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of real analysis as well as with classical harmonic analysis, including Calderón-Zygmund theory; also some knowledge of basic orthogonal polynomials theory would be convenient. The monograph  develops the main topics of classical harmonic analysis (semigroups, covering lemmas, maximal functions, Littlewood-Paley functions, spectral multipliers, fractional integrals and fractional derivatives, singular integrals) with respect to the Gaussian measure. The text provide an updated exposition, as self-contained as possible, of all the topics in Gaussian harmonic analysis that up to now are mostly scattered in research papers and sections of books; also an exhaustive bibliography for further reading.  Each chapter ends with a section of notes and further results where connections between Gaussian harmonic analysis and other connected fields, points of view and alternative techniques are given. Mathematicians and researchers in several areas will find the breadth and depth of the treatment of the subject highly useful.


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