An L 2 theory for differential forms on path spaces I
An L 2 theory for differential forms on path spaces I
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路径空间 I 上微分形式的 L 2 理论
DOI：
10.1016/j.jfa.2007.09.016
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发表时间：
2008
影响因子：
1.7
通讯作者：
Elworthy K
中科院分区：
文献类型：
--
作者：
Elworthy K
给出了具有布朗运动测度的黎曼流形M上连续路径的巴拿赫流形的一种微分形式理论。微分必须局限于特定的希尔伯特空间方向，即h -切向量。为了得到一个封闭的外部微分算子，对微分形式h型的相关空间进行m曲率的摄动，给出了l2h - 1型的Hodge分解，并描述了h - 2型的结构。根据h -切空间上的自然连接分析了对偶算子d *。Malliavin微积分是一个基本的工具。
An L2theory 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 L2H-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.