Lévy Laplacian of generalized functions on a nuclear space

DOI10.1016/0022-1236(90)90028-JzbMath0749.46029OpenAlexW2020631528MaRDI QIDQ1173576

Kimiaki Saitô, Hui-Hsiung Kuo, Nobuaki Obata

Publication date: 25 June 1992

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(90)90028-j

zbMATH Keywords

white noise calculusLévy Laplacianmean value propertyGross Laplacianregular polynomials

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Distributions on infinite-dimensional spaces (46F25)

Related Items (32)

Analytic characterizations of infinite dimensional distributions ⋮ Stochastic Lévy differential operators and Yang–Mills equations ⋮ CAUCHY PROBLEMS ASSOCIATED WITH THE LÉVY LAPLACIAN IN WHITE NOISE ANALYSIS ⋮ A SIMILARITY BETWEEN THE GROSS LAPLACIAN AND THE LÉVY LAPLACIAN ⋮ THE LÉVY LAPLACIAN ACTING ON POISSON NOISE FUNCTIONALS ⋮ Даламбертианы Леви и их применение в квантовой теории ⋮ Quantum Lévy Laplacian and associated heat equation ⋮ DIAGONALIZATION OF THE LÉVY LAPLACIAN AND RELATED STABLE PROCESSES ⋮ Infinite dimensional rotations and Laplacians in terms of white noise calculus ⋮ Applications of Lévy differential operators in the theory of gauge fields ⋮ Lévy Laplacians and instantons on manifolds ⋮ EXOTIC LAPLACIANS AND DERIVATIVES OF WHITE NOISE ⋮ White noise delta functions and infinite-dimensional Laplacians ⋮ HIERARCHY OF LÉVY–LAPLACIANS AND QUANTUM STOCHASTIC PROCESSES ⋮ Classical and nonclassical Levy Laplacians ⋮ A (C_o)-group generated by the lévy laplacian ⋮ A characterization of the geometric Brownian motion in terms of infinite dimensional Laplacians ⋮ STOCHASTIC HEAT EQUATION ON ALGEBRA OF GENERALIZED FUNCTIONS ⋮ Notes on a 𝐶₀-group generated by the Lévy Laplacian ⋮ Stochastic Processes Associated with a Sum of the Lévy Laplacians ⋮ A class of generalized Lévy Laplacians in infinite dimensional calculus ⋮ Lévy Laplacian on manifold and Yang-Mills heat flow ⋮ RENORMALIZED LAPLACIANS ON A CLASS OF HILBERT MANIFOLDS AND A BOCHNER–WEITZENBÖCK TYPE FORMULA FOR CURRENT GROUPS ⋮ Lévy Laplacians in Hida calculus and Malliavin calculus ⋮ NON-SELF-ADJOINT EXTENSIONS OF THE LÉVY–LAPLACIAN AND THE LÉVY–LAPLACE EQUATION ⋮ EXOTIC LAPLACIANS AND ASSOCIATED STOCHASTIC PROCESSES ⋮ Lévy differential operators and Gauge invariant equations for Dirac and Higgs fields ⋮ RENORMALIZED TRACES AS A LOOKING GLASS INTO INFINITE-DIMENSIONAL GEOMETRY ⋮ THE EXOTIC (HIGHER ORDER LÉVY) LAPLACIANS GENERATE THE MARKOV PROCESSES GIVEN BY DISTRIBUTION DERIVATIVES OF WHITE NOISE ⋮ The Lévy Laplacian and stable processes ⋮ A C₀-Group Generated by the Lévy Laplacian II ⋮ Rotation-invariant operators on white noise functionals

Cites Work

• Brownian functionals and applications
• Calculus on Gaussian white noise. I
• Calculus on Gaussian white noise. II
• Gaussian measures in Banach spaces
• Generalized multiple Wiener integrals
• The Fourier transform in white noise calculus
• Potential theory on Hilbert space
• A note on certain permutation groups in the infinite dimensional rotation group
• Ito’s formula and Levy’s Laplacian
• A characterization of the Lévy Laplacian in terms of infinite dimensional rotation groups
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