ar X iv : m at h / 06 12 41 6 v 1 [ m at h . PR ] 1 4 D ec 2 00 6 An L 2 theory for differential forms on path spaces I
نویسنده
چکیده
An L theory of differential forms is proposed for the Banach manifold of continuous paths on Riemannian manifolds 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 L 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.
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