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
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
Journal title :
Journal of Functional Analysis