Gaussian linear operators

DOI10.1007/BF01047837zbMath0808.46059OpenAlexW4244081193MaRDI QIDQ1320309

Denis Feyel, Arnaud De La Pradelle

Publication date: 5 June 1994

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01047837

zbMATH Keywords

Sobolev spacessemigroupsFock spaceMehler formulaGaussian measuressecond quantizationscapacitiesCameron-Martin spaceHilbert- Schmidt operatorsGaussian Lusinian locally convex spacelinear measurable operatorstightness of capacities

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Linear symmetric and selfadjoint operators (unbounded) (47B25) Linear operators on function spaces (general) (47B38) Measures and integration on abstract linear spaces (46G12) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Potentials and capacities on other spaces (31C15) Probability theory on linear topological spaces (60B11)

Related Items (5)

In memoriam Emile Bertin (1931-1994) ⋮ Brownian processes in infinite dimension ⋮ Generalized Mehler semigroups and applications ⋮ Gaussian measures on linear spaces ⋮ Stochastic integration of operator-valued functions with respect to Banach space-valued Brownian motion

Cites Work

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• On positive generalized functionals
• Espaces de Sobolev gaussiens. (Gaussian Sobolev spaces)
• Gaussian capacities
• An invariance result for capacities on Wiener space
• Sobolev spaces over the Wiener space based on an Ornstein-Uhlenbeck operator
• Littlewood-Paley theory on Gaussian spaces
• Linear Symmetries of Free Boson Fields
• Measurable Functions on Hilbert Space

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