Titlebook: Gaussian Harmonic Analysis; Wilfredo Urbina-Romero Book 2019 Springer Nature Switzerland AG 2019 Gaussian measure.Hermite polynomial expan

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書目名稱Gaussian Harmonic Analysis影響因子(影響力)




書目名稱Gaussian Harmonic Analysis影響因子(影響力)學(xué)科排名




書目名稱Gaussian Harmonic Analysis網(wǎng)絡(luò)公開度




書目名稱Gaussian Harmonic Analysis網(wǎng)絡(luò)公開度學(xué)科排名




書目名稱Gaussian Harmonic Analysis被引頻次




書目名稱Gaussian Harmonic Analysis被引頻次學(xué)科排名




書目名稱Gaussian Harmonic Analysis年度引用




書目名稱Gaussian Harmonic Analysis年度引用學(xué)科排名




書目名稱Gaussian Harmonic Analysis讀者反饋




書目名稱Gaussian Harmonic Analysis讀者反饋學(xué)科排名

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,The Ornstein–Uhlenbeck Operator and the Ornstein–Uhlenbeck Semigroup,sian harmonic analysis, to the Laplacian and the heat semigroup in the classical case. Then, we study an important property of the Ornstein–Uhlenbeck semigroup, the hypercontractivity property, and some of its applications.

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,Covering Lemmas, Gaussian Maximal Functions, and Calderón–Zygmund Operators,peration in analysis and to understand and simplify its study, maximal functions are introduced. Moreover, for any limit process such as almost sure convergence, there is a maximal function that controls it; therefore, the study of their properties is crucial.

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Gaussian Fractional Integrals and Fractional Derivatives, and Their Boundedness on Gaussian Functioe Ornstein–Uhlenbeck operator ., and then, Riesz and Bessel fractional derivatives. We study their regularity on Gaussian Lipschitz spaces, on Gaussian Besov–Lipschitz spaces, and on Gaussian Triebel–Lizorkin spaces. The results obtained are essentially similar to the classical results, as mentioned

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Preliminary Results: The Gaussian Measure and Hermite Polynomials, which are orthogonal polynomials, with respect to the Gaussian measure, and discuss in detail most of their properties. The interested reader will find the properties and identities of all classical orthogonal polynomials listed in the appendix.

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,The Poisson–Hermite Semigroup, study the characterization of the .-harmonic functions, the generalized Poisson–Hermite semigroups, and the conjugated Poisson–Hermite semigroup which, as in the classical case, is closely related to the notion of singular integrals.