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Gaussian Harmonic Analysis (Springer Monographs in Mathematics)

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en Limba Engleză Hardback – 04 Jul 2019
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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Specificații

ISBN-13: 9783030055967
ISBN-10: 3030055965
Pagini: 480
Dimensiuni: 155 x 235 mm
Greutate: 0.91 kg
Ediția: 1st ed. 2019
Editura: Springer
Colecția Springer
Seria Springer Monographs in Mathematics

Locul publicării: Cham, Switzerland

Cuprins

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.



Recenzii

“This well-written and organized (mainly self-contained) book is a reader-friendly manual in the field of Gaussian harmonic analysis. It can be recommended for experts and for graduate, postgraduate and doctoral students.” (Michael Perelmuter, zbMATH 1421.42001, 2019)

Textul de pe ultima copertă

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.


Caracteristici

Updated and self-contained exposition of all topics of Gaussian harmonic analysis that up to now are mostly scattered in research papers and sections of books
Gaussian harmonic analysis may serve as a good introduction to other possible harmonic analysis done for orthogonal expansion
A deep understanding of Gaussian harmonic analysis may help one gain insights into related problems in other non-euclidean settings