De Rham-Hodge-Kodaira operator on loop groups

DOI10.1006/jfan.1996.3077zbMath0901.58067OpenAlexW2073916277MaRDI QIDQ1368852

Shizan Fang, Jacques Franchi

Publication date: 26 November 1998

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

Full work available at URL: https://doi.org/10.1006/jfan.1996.3077

zbMATH Keywords

loop groupde Rham-Hodge-Kodaira operator

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes and stochastic analysis on manifolds (58J65)

Related Items (17)

Metrics \(\mathcal H_s\) and behaviours as \(s\downarrow \frac {1} {2}\) on loop groups ⋮ Hamilton-Jacobi semi-groups in infinite dimensional spaces ⋮ STOCHASTIC PROCESSES ON CLASSIFYING SPACES AND STRING STRUCTURES ⋮ The vanishing of \(L^2\) harmonic one-forms on based path spaces ⋮ Non-existence of infinitesimally invariant measures on loop groups ⋮ An \(L^{2}\) theory for differential forms on path spaces. I ⋮ SOME FAMILIES OF q-VECTOR FIELDS ON PATH SPACES ⋮ WITTEN LAPLACIAN ON PINNED PATH GROUP AND ITS EXPECTED SEMICLASSICAL BEHAVIOR ⋮ Connections and curvature in the Riemannian geometry of configuration spaces ⋮ Weak Levi-Civita connection for the damped metric on the Riemannian path space and vanishing of Ricci tensor in adapted differential geometry ⋮ A STOCHASTIC APPROACH TO THE EULER–POINCARE CHARACTERISTIC OF A QUOTIENT OF A LOOP GROUP ⋮ Vanishing of one-dimensional \(L^2\)-cohomologies of loop groups ⋮ Integration by parts formula and logarithmic Sobolev inequality on the path space over loop groups ⋮ Stochastic equivariant cohomologies and cyclic cohomology ⋮ Riemannian distance, Rademacher theorem and transportation cost inequality on loop groups. ⋮ Modulus of continuity of the canonic Brownian motion ``on the group of diffeomorphisms of the circle ⋮ Weitzenböck and Clark-Ocone Decompositions for Differential Forms on the Space of Normal Martingales

Cites Work

• Integration on loop groups. I: Quasi invariant measures
• Differential calculus on finite codimensional submanifolds of the Wiener space: The divergence operator
• De Rham-Hodge-Kodaira's decomposition on an abstract Wiener space
• The geometry of loop groups
• Logarithmic Sobolev inequalities on loop groups
• Integration on loop groups. II: Heat equation for the Wiener measure
• Integration on loop groups. III: Asymptotic Peter-Weyl orthogonality
• On the Ornstein-Uhlenbeck operators on Wiener-Riemannian manifolds
• Renormalized differential geometry on path space: Structural equation, curvature
• Sobolev spaces over loop groups
• Stochastic anticipative integrals on a Riemannian manifold
• Logarithmic Sobolev inequalities for pinned loop groups
• Certain gradient flows and submanifolds in Wiener spaces
• Uniqueness of ground states for Schrödinger operators over loop groups
• The divergence on submanifolds of the Wiener space
• A Cameron-Martin Type Quasi-Invariance Theorem for Pinned Brownian Motion on a Compact Riemannian Manifold
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