A Poincaré inequality on loop spaces

DOI10.1016/j.jfa.2010.05.006zbMath1228.58017arXiv0905.3007OpenAlexW2162074224WikidataQ126163753 ScholiaQ126163753MaRDI QIDQ990153

Xue-Mei Li, Xin Chen, Bo Wu

Publication date: 6 September 2010

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

Full work available at URL: https://arxiv.org/abs/0905.3007

zbMATH Keywords

Malliavin calculusPoincaré inequalityloop spaceBrownian bridge measure

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Stochastic calculus of variations and the Malliavin calculus (60H07) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (5)

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 \(\mathbb{L}^1 \) ⋮ Logarithmic heat kernel estimates without curvature restrictions ⋮ A concrete estimate for the weak Poincaré inequality on loop space ⋮ Functional inequality on path space over a non-compact Riemannian manifold

Cites Work

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• Integration on loop groups. I: Quasi invariant measures
• Heat kernel analysis on infinite-dimensional Heisenberg groups
• Logarithmic Sobolev inequalities on loop groups
• Integration on loop groups. II: Heat equation for the Wiener measure
• A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold
• Uniform positivity improving property, Sobolev inequalities, and spectral gaps
• Differential calculus on path and loop spaces. II: Irreducibility of Dirichlet forms on loop spaces
• Logarithmic Sobolev inequalities and exponential integrability
• Stochastic differential equations on noncompact manifolds: Moment stability and its topological consequences
• Integration by parts and quasi-invariance for heat kernel measures on loop groups
• Integration by parts in loop spaces
• Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces
• Absence of spectral gaps on a class of loop spaces
• Local spectral gaps on loop spaces.
• Integration by parts for heat measures over loop groups
• Logarithmic derivatives of heat kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients on loop spaces
• Exponential decay of positivity preserving semigroups on \(L^p\)
• Absolute continuity of heat kernel measure with pinned Wiener measure on loop groups
• Pinned Brownian motion and its perturbations
• Logarithmic Sobolev inequalities for pinned loop groups
• Itô maps and analysis on path spaces
• Weak logarithmic Sobolev inequalities and entropic convergence
• Equivalence of heat kernel measure and pinned Wiener measure on loop groups
• A note on the isoperimetric constant
• Logarithmic Sobolev Inequalities
• 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
• A Simple Analytic Proof of an Inequality by P. Buser
• On Extensions of Myers' Theorem
• 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
• Weak Poincaré inequalities and \(L^2\)-convergence rates of Markov semigroups

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