Title of article :
An L2 theory for differential forms on path spaces I ✩
Author/Authors :
K.D. Elworthy، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2008
Pages :
50
From page :
196
To page :
245
Abstract :
An L2 theory of differential forms is proposed for the Banach manifold of continuous paths on a Riemannian manifold M furnished with its Brownian motion measure. Differentiation must be restricted to certain Hilbert space directions, the H-tangent vectors. To obtain a closed exterior differential operator the relevant spaces of differential forms, the H-forms, are perturbed by the curvature of M. A Hodge decomposition is given for L2 H-one-forms, and the structure of H-two-forms is described. The dual operator d∗ is analysed in terms of a natural connection on the H-tangent spaces. Malliavin calculus is a basic tool. © 2007 Elsevier Inc. All rights reserved.
Keywords :
Path space , L2 cohomology , Hodge decomposition , Malliavin calculus , Banach manifolds , Itô map , Markovian connection , Exterior products , Infinite dimensional , Curvature , Bismut tangentspaces , Differential forms
Journal title :
Journal of Functional Analysis
Serial Year :
2008
Journal title :
Journal of Functional Analysis
Record number :
839549
Link To Document :
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