The log-Sobolev inequality on loop space over a compact Riemannian manifold

DOI10.1006/jfan.1998.3263zbMath0909.22036OpenAlexW1996923978MaRDI QIDQ1268078

Fu-Zhong Gong, Zhi-Ming Ma

Publication date: 14 October 1998

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

Full work available at URL: https://doi.org/10.1006/jfan.1998.3263

zbMATH Keywords

Riemannian manifoldheat kernellog-Sobolev inequalityloop spacemartingale representation theoremClark-Ocone-Haussman formula

Mathematics Subject Classification ID

Loop groups and related constructions, group-theoretic treatment (22E67) Diffusion processes and stochastic analysis on manifolds (58J65)

Related Items (14)

Martingale representation and logarithmic-Sobolev inequality for the fractional Ornstein-Uhlenbeck measure ⋮ On the characterization of Brownian bridge measure on the pinned path space over a compact Riemannian manifold ⋮ Asymptotics of spectral gaps on loop spaces over a class of Riemannian manifolds ⋮ Log-Hessian and deviation bounds for Markov semi-groups, and regularization effect in \(\mathbb{L}^1 \) ⋮ Stochastic Heat Equations with Values in a Manifold via Dirichlet Forms ⋮ Logarithmic heat kernel estimates without curvature restrictions ⋮ Absence of spectral gaps on a class of loop spaces ⋮ Local spectral gaps on loop spaces. ⋮ On a certain semiclassical problem on Wiener spaces ⋮ A concrete estimate for the weak Poincaré inequality on loop space ⋮ Semi-classical limit of the bottom of spectrum of a Schrödinger operator on a path space over a compact Riemannian manifold ⋮ An estimate of the gap of spectrum of Schrödinger operators which generate hyperbounded semigroups ⋮ Poincaré inequality for weighted first order Sobolev spaces on loop spaces ⋮ Logarithmic derivatives of heat kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients on loop spaces

Cites Work

• Short time behavior of the heat kernel and its logarithmic deviatives
• Some estimates of the transition density of a nondegenerate diffusion Markov process
• Precise asymptotics of certain Wiener functionals
• Logarithmic Sobolev inequalities on loop groups
• Integration by parts in loop spaces
• Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces
• Renormalized differential geometry on path space: Structural equation, curvature
• Integration by parts for pinned Brownian motion
• Pinned Brownian motion and its perturbations
• Logarithmic Sobolev inequalities for pinned loop groups
• Martingale representation and log-Sobolev inequality on loop space
• A Cameron-Martin Type Quasi-Invariance Theorem for Pinned Brownian Motion on a Compact Riemannian Manifold
• Riemannian geometry
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