Logarithmic Sobolev inequalities on Lie groups

zbMath0761.46019MaRDI QIDQ1203510

Leonard Gross

Publication date: 10 February 1993

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Lie algebraheat kernelbasisBrownian motion on a Lie groupconnected finite dimensional Lie groupGaussian constant fails to be best possiblegroup valued random walklogarithmic Sobolev inequality for the energy form

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Diffusion processes and stochastic analysis on manifolds (58J65) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Measures (Gaussian, cylindrical, etc.) on manifolds of maps (58D20)

Related Items (7)

Hamilton-Jacobi semi-groups in infinite dimensional spaces ⋮ Logarithmic Sobolev inequalities on non-isotropic Heisenberg groups ⋮ On logarithmic Sobolev inequalities for the heat kernel on the Heisenberg group ⋮ Small-time Gaussian behavior of symmetric diffusion semigroups ⋮ Logarithmic Sobolev inequalities on loop groups ⋮ Transportation cost inequalities on path and loop groups ⋮ Optimal transport maps on infinite dimensional spaces

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