An <textbox>L²textbox> theory for differential forms on path spaces I

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• 作者：K.D. Elworthy ; Xue-Mei Li
• 关键词：Path space ; style=""text-decoration ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6WJJ-4R2HKYD-2&_mathId=mml5&_user=10&_cdi=6880&_rdoc=5&_acct=C000050221&_version=1&_userid=10&md5=e7c5e5de826e409c1c25c77a613db2d
• 刊名：Journal of Functional Analysis
• 出版年：2008
• 出版时间：1 January 2008
• 年：2008
• 卷：254
• 期：1
• 页码：196-245
• 全文大小：428 K

文摘

An style=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6WJJ-4R2HKYD-2&_mathId=mml2&_user=10&_cdi=6880&_rdoc=5&_acct=C000050221&_version=1&_userid=10&md5=05f4ef2a159bdeabcb45b5b0a4f0b23f"" title=""Click to view the MathML source"">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 style=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6WJJ-4R2HKYD-2&_mathId=mml3&_user=10&_cdi=6880&_rdoc=5&_acct=C000050221&_version=1&_userid=10&md5=e0eaec3bbb574835868e21119841bd94"" title=""Click to view the MathML source"">L² H-one-forms, and the structure of H-two-forms is described. The dual operator style=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6WJJ-4R2HKYD-2&_mathId=mml4&_user=10&_cdi=6880&_rdoc=5&_acct=C000050221&_version=1&_userid=10&md5=1e3b72ba8f9f0eca3f9e80856142b477"" title=""Click to view the MathML source"">d^* is analysed in terms of a natural connection on the H-tangent spaces. Malliavin calculus is a basic tool.