Transformations on white noise functions associated with second order differential operators of diagonal type

DOI10.1017/S0027763000006590zbMath0912.60084MaRDI QIDQ3839745

Nobuaki Obata, Un Cig Ji, Dong Myung Chung

Publication date: 18 May 1999

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

number operatorGross Laplacianwhite noise functionsone-parameter transformation group

Mathematics Subject Classification ID

Generalized stochastic processes (60G20) Linear operators on function spaces (general) (47B38) Stochastic analysis (60H99) Distributions on infinite-dimensional spaces (46F25)

Related Items (6)

CAUCHY PROBLEMS ASSOCIATED WITH THE LÉVY LAPLACIAN IN WHITE NOISE ANALYSIS ⋮ Two generalizations of Mehler's formula in white noise analysis ⋮ An analytic characterization of \((p,q)\)-white noise functionals ⋮ UNITARITY OF KUO'S FOURIER–MEHLER TRANSFORM ⋮ Multi-parameter transformation groups on white noise functionals ⋮ Higher Powers of Quantum White Noises in Terms of Integral Kernel Operators

Cites Work

• Unnamed Item
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• Rotation-invariant operators on white noise functionals
• De Rham-Hodge-Kodaira decomposition in \(\infty\)-dimensions
• Transformations for white noise functionals
• White noise calculus and Fock space
• Constructing one-parameter transformations on white noise functions in terms of equicontinuous generators
• On the Laplacian on a space of white noise functionals
• Potential theory on Hilbert space
• A fundamental solution of the parabolic equation on Hilbert space
• On the infinite dimensional Laplacian operator
• Infinite dimensional rotations and Laplacians in terms of white noise calculus
• Transforms on white noise functionals with their applications to Cauchy problems

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