Rotation-invariant operators on white noise functionals

DOI10.1007/BF02571783zbMath0735.46031MaRDI QIDQ811508

Nobuaki Obata

Publication date: 1992

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174388

zbMATH Keywords

Riemannian manifoldrenormalizationwhite noise calculusannihilation operatorGaussian measureGâteaux derivativeGelfand tripleinfinite dimensional rotation groupdistributions as integral kernelsGross Laplaciansgroup-theoretical characterization of the infinite dimensional LaplaciansHilbert-Schmidt typenumber operatorsrotation- invariant distributionsrotation-invariant operators acting on the white noise functionalsWick-ordering

Mathematics Subject Classification ID

Renormalization group methods applied to problems in quantum field theory (81T17) Applications of functional analysis in quantum physics (46N50) Measures and integration on abstract linear spaces (46G12) Distributions on infinite-dimensional spaces (46F25)

Related Items (11)

Evolution systems and continuity equations for white noise functionals ⋮ The characterizations of Laplacians in white noise analysis ⋮ Products and transforms of white-noise functionals (in general setting) ⋮ White noise delta functions and continuous version theorem ⋮ Derivations on white noise functionals ⋮ Fractional Langevin type equations for white noise distributions ⋮ Rotation invariance of quantum Laplacians ⋮ Transformations on white noise functions associated with second order differential operators of diagonal type ⋮ Multi-parameter transformation groups on white noise functionals ⋮ Higher Powers of Quantum White Noises in Terms of Integral Kernel Operators ⋮ Some cauchy problems in white noise analysis and associated semigroups of operators

Cites Work

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• Lévy Laplacian of generalized functions on a nuclear space
• Transformations for white noise functionals
• Potential theory on Hilbert space
• On the infinite dimensional Laplacian operator
• Quantum white noises—White noise approach to quantum stochastic calculus
• Infinite dimensional rotations and Laplacians in terms of white noise calculus
• A characterization of the Lévy Laplacian in terms of infinite dimensional rotation groups

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