An \(L^{2}\) theory for differential forms on path spaces. I

DOI10.1016/j.jfa.2007.09.016zbMath1141.58020arXivmath/0612416OpenAlexW2071492286MaRDI QIDQ2469820

Xue-Mei Li, K. David Elworthy

Publication date: 11 February 2008

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

Full work available at URL: https://arxiv.org/abs/math/0612416

zbMATH Keywords

Malliavin calculusHodge decomposition\(L^2\) cohomologyPath spaceBismut tangent spacesExterior products

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Stochastic calculus of variations and the Malliavin calculus (60H07) Hodge theory in global analysis (58A14)

Related Items (5)

Heat flow on 1-forms under lower Ricci bounds. Functional inequalities, spectral theory, and heat kernel ⋮ The vanishing of \(L^2\) harmonic one-forms on based path spaces ⋮ Using Witten Laplacians to Locate Index-1 Saddle Points ⋮ Vanishing of one-dimensional \(L^2\)-cohomologies of loop groups ⋮ Functional inequalities on path space of sub-Riemannian manifolds and applications

Cites Work

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• De Rham-Hodge-Kodaira decomposition in \(\infty\)-dimensions
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• The Lie bracket of adapted vector fields on Wiener spaces
• De Rham-Hodge-Kodaira operator on loop groups
• Vector fields on mapping spaces and related Dirichlet forms and diffusions
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