کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4591700 | 1335047 | 2008 | 50 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An L2 theory for differential forms on path spaces I
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 254, Issue 1, 1 January 2008, Pages 196-245
Journal: Journal of Functional Analysis - Volume 254, Issue 1, 1 January 2008, Pages 196-245