کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4592836 1335151 2008 50 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The Taylor map on complex path groups
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
The Taylor map on complex path groups
چکیده انگلیسی

Let W(G) denote the path group of an arbitrary complex connected Lie group. The existence of a heat kernel measure νt on W(G) has been shown in [M. Cecil, B.K. Driver, Heat kernel measure on loop and path groups, preprint, http://www.math.uconn.edu/~cecil/papers/p2.pdf; Infin. Dimens. Anal. Quantum Probab. Relat. Top., submitted for publication]. The present work establishes an isometric map, the Taylor map, from the space of L2(νt)-holomorphic functions on W(G) to a subspace of the dual of the universal enveloping algebra of Lie(H(G)), where H(G) is the Lie subgroup of finite energy paths. This map is shown to be surjective in the case where G is a simply connected graded Lie group.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 254, Issue 2, 15 January 2008, Pages 318-367