Two generalizations of Mehler's formula in white noise analysis

DOI10.1080/17442508.2022.2089039zbMath1525.60087WikidataQ113848395 ScholiaQ113848395MaRDI QIDQ6115723

Wolfgang Bock, Maximilian Böck

Publication date: 13 July 2023

Published in: Stochastics (Search for Journal in Brave)

zbMATH Keywords

white noise analysisnumber operatorMehler's formulaGross LaplacianFourier-Gauss transformgeneralized Wick tensors

Mathematics Subject Classification ID

Generalized stochastic processes (60G20) White noise theory (60H40)

Cites Work

• Fourier-Mehler transforms of generalized Brownian functionals
• Integral transforms of analytic functions on abstract Wiener spaces
• On Fourier transform of generalized Brownian functionals
• Transformations for white noise functionals
• White noise calculus and Fock space
• Spaces of white noise distributions: Constructions, descriptions, applications. I
• Transformation groups on white noise functionals and their applications
• Generalized functionals in Gaussian spaces: The characterization theorem revisited
• Fourier-Wiener transforms of analytic functionals
• A white noise approach to phase space Feynman path integrals
• Let Us Use White Noise
• A NOTE ON CONVOLUTION OPERATORS IN WHITE NOISE CALCULUS
• Transformations on white noise functions associated with second order differential operators of diagonal type
• Infinite dimensional rotations and Laplacians in terms of white noise calculus
• Unitarity of Generalized Fourier–Gauss Transforms
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