Wick and Anti-Wick Characterizations of Linear Operators on Spaces of Power Series Expansions

Abstract

We study links between Wick, anti-Wick and analytic kernel operators on the Bargmann transform side. We consider classes of kernels, whose corresponding operators agree with the sets of linear and continuous operators on spaces of power series expansions, which are Bargmann images of Pilipović spaces. We show that in several situations, the sets of Wick and kernel operators with symbols and kernels in such classes agree. We also find suitable subclasses to these kernel classes, whose corresponding sets of Wick and anti-Wick operators agree. We also show ring, module and composition properties for such classes.