Gaussian Harmonic Analysis. 1st ed. 2019

種類:

電子ブック

責任表示:

by Wilfredo Urbina-Romero

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2019

著者名:

• Urbina-Romero, Wilfredo.
• SpringerLink (Online service)

シリーズ名:

Springer Monographs in Mathematics ;

ISBN:

9783030055974 [3030055973]    

注記:

Chapter 1- Preliminary Results -- Chapter 2- The Ornstein-Uhlenbeck Operator and the Ornstein-Uhlenbeck Semigroup -- Chapter 3- The Poisson-Hermite Semigroup -- Chapter 4- Covering Lemmas, Gaussian Maximal Functions, and Calderón-Zygmund Operators -- Chapter 5- Littlewood-Paley-Stein Theory with respect to γd -- Chapter 6- Spectral Multiplier Operators with respect to γd -- Chapter 7- Function Spaces with respect to γd -- Chapter 8- Gaussian Fractional Integrals and Fractional Derivatives -- Chapter 9- Singular Integrals with respect to γd -- Appendix -- References -- Index.
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 analys

ローカル注記:

学内専用E-BOOKS (local access only)