# Gaussian Harmonic Analysis

- 1 Citations
- 7 Mentions
- 7.1k Downloads

Part of the Springer Monographs in Mathematics book series (SMM)

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- 1 Citations
- 7 Mentions
- 7.1k Downloads

Part of the Springer Monographs in Mathematics book series (SMM)

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.

Gaussian measure Hermite polynomial expansions Ornstein-Uhlenbeck operator Ornstein-Uhlenbeck semigroup Poisson-Hermite semigroup covering lemmas for the Gaussian measure maximal functions with respect to the Gaussian measure Gaussian Littlewood-Paley functions Gaussian spectral multipliers Gaussian fractional integrals and fractional derivatives Gaussian singular integrals

- DOI https://doi.org/10.1007/978-3-030-05597-4
- Copyright Information Springer Nature Switzerland AG 2019
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-3-030-05596-7
- Online ISBN 978-3-030-05597-4
- Series Print ISSN 1439-7382
- Series Online ISSN 2196-9922
- Buy this book on publisher's site