The generalized $\partial$-complex on the Segal Bargmann space

Abstract

We study certain densely defined unbounded operators on the Segal-Barg\-mann space, related to the annihilation and creation operators of quantum mechanics. We consider the corresponding $D$-complex and study properties of the corresponding complex Laplacian ${\tilde{\square }}_D=D{D}^{\ast }+D^{\ast }D,$ where $D$ is a differential operator of polynomial type.

8 pages