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An L-2 theory for differential forms on path spaces I
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Elworthy, K. D. and Li, X-M. (2008) An L-2 theory for differential forms on path spaces I. Journal of Functional Analysis, Vol.254 (No.1). pp. 196-245. doi:10.1016/j.jfa.2007.09.016 ISSN 0022-1236.
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Official URL: http://dx.doi.org/10.1016/j.jfa.2007.09.016
Abstract
An L-2 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 L-2 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. (c) 2007 Elsevier Inc. All rights reserved.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Differential forms, Malliavin calculus, Banach manifolds, Curvature, Infinite-dimensional manifolds, Hodge theory, Homology theory | ||||
Journal or Publication Title: | Journal of Functional Analysis | ||||
Publisher: | Academic Press | ||||
ISSN: | 0022-1236 | ||||
Official Date: | 1 January 2008 | ||||
Dates: |
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Volume: | Vol.254 | ||||
Number: | No.1 | ||||
Number of Pages: | 50 | ||||
Page Range: | pp. 196-245 | ||||
DOI: | 10.1016/j.jfa.2007.09.016 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), European Union (EU), Royal Society (Great Britain), National Science Foundation (U.S.) (NSF), Alexander von Humboldt-Stiftung | ||||
Grant number: | GR/NOO 845 (EPSRC), ERB-FMRX-CT96- 0075 (EU), DMS 0072387 (NSF) |
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