Constructing one-parameter transformations on white noise functions in terms of equicontinuous generators

DOI10.1007/BF01319042zbMath0909.46041MaRDI QIDQ1376011

Nobuaki Obata

Publication date: 8 April 1999

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178793

zbMATH Keywords

power seriesone-parameter group of operatorsbarrelled locally convex spaceCauchy problems in white noise (Gaussian) spaceequicontinuous generatorlinear combination of the number operator and the Gross Laplacianlocally equicontinuous holomorphic one-parameter groups of operatorswhite noise functions

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Groups and semigroups of linear operators (47D03) Linear operators on function spaces (general) (47B38) Stochastic analysis (60H99) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15) Distributions on infinite-dimensional spaces (46F25)

Related Items (5)

Evolution systems and continuity equations for white noise functionals ⋮ Fractional Langevin type equations for white noise distributions ⋮ Transformations on white noise functions associated with second order differential operators of diagonal type ⋮ Multi-parameter transformation groups on white noise functionals ⋮ Wick calculus for vector-valued Gaussian white noise unctionals

Cites Work

• Transformations for white noise functionals
• White noise calculus and Fock space
• Potential theory on Hilbert space
• Infinite dimensional rotations and Laplacians in terms of white noise calculus
• Parabolic Equations Associated with the Number Operator
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