Title: Holomorphic methods in analysis
Speaker: Professor Brian Hall, UCSD
Abstract: The Segal-Bargmann transform, developed independently by Segal and Bargmann in the early 1960's, is a unitary map between L^2(R^n) and a certain L^2 space of holomorphic functions on C^n. Segal was concerned with the infinite-dimensional (n = infinity) case of this.Date: Friday, February 13, 1998
In In the first part of my talk I will describe a generalization of the Segal-Bargmann transform, in which R^n is replaced by a compact Lie group K, and C^n is replaced by the complexification of K. I will mention certain results about this transform which support a particular physical interpretation of it. In the second part of my talk I will describe extensions of the transform to the setting of path-groups. One instance of this has application to the quantization of Yang-Mills theory on a space-time cylinder.