Certain properties of the domains of multiplication and differentiation operators on a generalized Segal-Bargmann space

Abstract

The Segal-Bargmann space is the space of all holomorphic functions on Cd which are square-integrable with respect to a Guassian measure. We study certain properties of the domains of multiplicaion and differentiation operators on the Segal-Bargmann space. Then we extend these results to those of a generalized Segal-Bargmann space, where we replace the Guassian measure by a measure with a desity function which decays faster than the Guassian factor near infinity.