A characterization of the Lévy Laplacian in terms of infinite dimensional rotation groups

DOI10.1017/S0027763000003020zbMath0682.22015OpenAlexW1525057503MaRDI QIDQ4731396

Nobuaki Obata

Publication date: 1990

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0027763000003020

zbMATH Keywords

rotation groupsemidirect productLévy Laplacian

Mathematics Subject Classification ID

Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Diffusion processes and stochastic analysis on manifolds (58J65) Analysis on other specific Lie groups (43A80)

Related Items (18)

CAUCHY PROBLEMS ASSOCIATED WITH THE LÉVY LAPLACIAN IN WHITE NOISE ANALYSIS ⋮ A SIMILARITY BETWEEN THE GROSS LAPLACIAN AND THE LÉVY LAPLACIAN ⋮ 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 ⋮ Lévy Laplacians and instantons on manifolds ⋮ Lévy Laplacian of generalized functions on a nuclear space ⋮ EXOTIC LAPLACIANS AND DERIVATIVES OF WHITE NOISE ⋮ White noise delta functions and infinite-dimensional Laplacians ⋮ 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 ⋮ EXOTIC LAPLACIANS AND ASSOCIATED STOCHASTIC PROCESSES ⋮ A QUANTUM APPROACH TO LAPLACE OPERATORS ⋮ 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

• Unnamed Item
• Density of natural numbers and the Lévy group
• Einige Sätze über messbare Abbildungen
• Potential theory on Hilbert space
• Operators commuting with a von Neumann algebra modulo the set of compact operators
• Operator methods in classical mechanics. II
• A note on certain permutation groups in the infinite dimensional rotation group
• ON MEANS AND THE LAPLACIAN OF FUNCTIONS ON HILBERT SPACE

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