Complex symmetry of differential operators on generalized Fock spaces

Abstract

In this paper, we classify the family of entire functions [Formula: see text] such that the induced weighted composition map [Formula: see text], is a conjugation namely [Formula: see text], where [Formula: see text] is an arbitrary complex number and [Formula: see text] is a real number such that [Formula: see text]. In the last section, we characterize the [Formula: see text]-symmetric maximal differential operators on the Fock space [Formula: see text].