Derivations on white noise functionals

DOI10.1017/S0027763000005286zbMath0841.46030MaRDI QIDQ4869958

Nobuaki Obata

Publication date: 17 March 1996

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

zbMATH Keywords

annihilation operatorGelfand tripleGaussian spaceintegral kernel operators\((E)^*\)-valued distributionfirst-order differential operator with distribution coefficientsspaces of test and generalized functionsstandard triple of white noise functionals

Mathematics Subject Classification ID

Linear operators on function spaces (general) (47B38) Derivatives of functions in infinite-dimensional spaces (46G05) Stochastic analysis (60H99) Distributions on infinite-dimensional spaces (46F25) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)

Related Items (3)

QWN-EULER OPERATOR AND ASSOCIATED CAUCHY PROBLEM ⋮ Operator theory: quantum white noise approach ⋮ QWN-first-order Wick differential operators and an associated transport equation

Cites Work

• Rotation-invariant operators on white noise functionals
• Dirichlet forms and white noise analysis
• Transformations for white noise functionals
• An analytic characterization of symbols of operators on white noise functionals
• Operator calculus on vector-valued white noise functionals
• A remark on the space of testing random variables in the white noise calculus
• Infinite dimensional rotations and Laplacians in terms of white noise calculus

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