The Taylor map on complex path groups

DOI10.1016/j.jfa.2007.09.018zbMath1133.22002OpenAlexW2049853599MaRDI QIDQ2469824

Matthew Cecil

Publication date: 11 February 2008

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

Full work available at URL: https://escholarship.org/uc/item/96b980b3

zbMATH Keywords

path groupdiffusionssurjectivitygraded Lie algebraheat kernel measureTaylor mapBaker-Campbell-Hausdorff seriesmultilinear functionssimply connected complex Lie groupholomorphic cylinder functionsincrements of pathsskeleton theoremTaylor isometry

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Set functions and measures on topological groups or semigroups, Haar measures, invariant measures (28C10)

Related Items (6)

A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groups ⋮ Holomorphic functions and the Itô chaos ⋮ Dimension-independent estimates for heat operators and harmonic functions ⋮ Square integrable holomorphic functions on infinite-dimensional Heisenberg type groups ⋮ The Ricci curvature of finite dimensional approximations to loop and path groups ⋮ Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mathematical characterization of the physical vacuum for a linear Bose- Einstein field
• Holomorphic functions and subelliptic heat kernels over Lie groups
• Nilpotent Lie groups: Structure and applications to analysis
• White noise calculus and Fock space
• Properties of holomorphic Wiener functions -- skeleton, contraction, and local Taylor expansion
• Integration by parts and quasi-invariance for heat kernel measures on loop groups
• The Segal-Bargmann transform for path-groups
• Generalized functions on infinite dimensional spaces and its applications to white noise calculus
• Absolute continuity of heat kernel measure with pinned Wiener measure on loop groups
• On the Kakutani-Itô-Segal-Gross and Segal-Bargmann-Hall isomorphisms
• Logarithmic Sobolev inequalities for pinned loop groups
• Heat kernel analysis of Cameron-Martin subgroup for infinite dimensional groups
• Tensor Algebras Over Hilbert Spaces. I
• HEAT KERNEL MEASURE ON LOOP AND PATH GROUPS
• TAYLOR MAP ON GROUPS ASSOCIATED WITH A II₁-FACTOR
• On a Hilbert Space of Analytie Functions and an Associated Integral Transform. Part II. A Family of Related Function Spaces Application to Distribution Theory
• Lie groups

This page was built for publication: The Taylor map on complex path groups