CAUCHY PROBLEMS ASSOCIATED WITH THE LÉVY LAPLACIAN IN WHITE NOISE ANALYSIS

DOI10.1142/S0219025799000072zbMath0936.46033OpenAlexW2030574274MaRDI QIDQ4269412

Dong Myung Chung, Kimiaki Seitô, Un Cig Ji

Publication date: 29 November 1999

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025799000072

zbMATH Keywords

Lévy Laplacianexistence and the uniquenessheat type equationspace of generalized white noise functionals

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) General theory of partial differential operators (47F05) White noise theory (60H40) Distributions on infinite-dimensional spaces (46F25)

Related Items (14)

A SIMILARITY BETWEEN THE GROSS LAPLACIAN AND THE LÉVY LAPLACIAN ⋮ THE LÉVY LAPLACIAN ACTING ON POISSON NOISE FUNCTIONALS ⋮ Quantum Lévy Laplacian and associated heat equation ⋮ DIAGONALIZATION OF THE LÉVY LAPLACIAN AND RELATED STABLE PROCESSES ⋮ EXOTIC LAPLACIANS AND DERIVATIVES OF WHITE NOISE ⋮ White noise delta functions and infinite-dimensional Laplacians ⋮ 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 ⋮ Higher order multi-dimensional extensions of Cesàro theorem ⋮ EXOTIC LAPLACIANS AND ASSOCIATED STOCHASTIC PROCESSES ⋮ THE EXOTIC (HIGHER ORDER LÉVY) LAPLACIANS GENERATE THE MARKOV PROCESSES GIVEN BY DISTRIBUTION DERIVATIVES OF WHITE NOISE ⋮ The Lévy Laplacian and stable processes

Cites Work

• Lévy Laplacian of generalized functions on a nuclear space
• A characterization of Hida distributions
• Transformations for white noise functionals
• An analytic characterization of symbols of operators on white noise functionals
• Transformation groups on white noise functionals and their applications
• Ito’s formula and Levy’s Laplacian
• Transformations on white noise functions associated with second order differential operators of diagonal type
• Infinite dimensional rotations and Laplacians in terms of white noise calculus
• A C₀-Group Generated by the Lévy Laplacian II
• Transforms on white noise functionals with their applications to Cauchy problems
• A characterization of the Lévy Laplacian in terms of infinite dimensional rotation groups

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