LOGARITHMIC SOBOLEV INEQUALITY FOR $H_0^s$-METRIC ON PINNED LOOP GROUPS

DOI10.1142/S0219025704001505zbMath1050.60055OpenAlexW2032403492MaRDI QIDQ4474480

Yuzuru Inahama

Publication date: 12 July 2004

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/s0219025704001505

zbMATH Keywords

logarithmic Sobolev inequalityRicci tensorheat kernel measure\(H^s_0\)-metricpinned loop group

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) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (2)

Heat kernel analysis on infinite-dimensional Heisenberg groups ⋮ Heat kernel analysis on semi-infinite Lie groups

Cites Work

• The geometry of loop groups
• Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces
• Integration by parts for heat measures over loop groups
• Integration by parts formula and logarithmic Sobolev inequality on the path space over loop groups
• Convergence of finite dimensional distributions of heat kernel measures on loop groups
• Logarithmic Sobolev inequalities for pinned loop groups
• A logarithmic Sobolev inequality for the free loop group
• Logarithmic Sobolev inequality on free loop groups for heat kernel measures associated with the general Sobolev spaces

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