Heat kernel analysis of Cameron-Martin subgroup for infinite dimensional groups

DOI10.1006/jfan.1999.3505zbMath1041.46027OpenAlexW2089158521MaRDI QIDQ1971937

Maria Gordina

Publication date: 28 August 2000

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

Full work available at URL: https://doi.org/10.1006/jfan.1999.3505

zbMATH Keywords

stochastic differential equationinfinite-dimensional Lie algebraholomorphic functionheat kernel measuretensor algebrainfinite-dimensional groupCameron-Martin subgroupHilbert-Schmidt orthogonal groupHilbert-Schmidt symplectic group

Mathematics Subject Classification ID

Infinite-dimensional holomorphy (46G20) Analysis on real and complex Lie groups (22E30) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Lie algebras of Lie groups (22E60) Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Spaces of differentiable or holomorphic functions on infinite-dimensional spaces (46E50) Applications of functional analysis to differential and integral equations (46N20) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (13)

Harmonic analysis with respect to heat kernel measure ⋮ Holomorphic functions and subelliptic heat kernels over Lie groups ⋮ The two-parameter free unitary Segal-Bargmann transform and its Biane-Gross-Malliavin identification ⋮ TAYLOR MAP ON GROUPS ASSOCIATED WITH A II₁-FACTOR ⋮ Beyond Haar and Cameron-Martin: the Steinhaus support ⋮ A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groups ⋮ Holomorphic functions and the Itô chaos ⋮ The large-\(N\) limit of the Segal-Bargmann transform on \(\mathbb U_N\) ⋮ The Taylor map on complex path groups ⋮ Square integrable holomorphic functions on infinite-dimensional Heisenberg type groups ⋮ Heat kernel analysis on infinite-dimensional Heisenberg groups ⋮ Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups ⋮ Hilbert--Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometry

Cites Work

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• On the Kakutani-Itô-Segal-Gross and Segal-Bargmann-Hall isomorphisms
• On a Hilbert space of analytic functions and an associated integral transform part I
• REMARKS ON A HILBERT SPACE OF ANALYTIC FUNCTIONS
• Stochastic Equations in Infinite Dimensions

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