2-complex symmetric weighted composition operators on Fock space

Abstract

The aim of the present paper is to completely characterize 2-complex symmetric weighted composition operators $ W_{e^{\overline{p}z, az+b}} $ with the conjugations $ C $ and $ C_{r, s, t} $ defined by $ Cf(z) = \overline{f(\bar{z})} $ and $ C_{r, s, t}f(z) = te^{sz}\overline{f(\overline{rz+s})} $ on Fock space by building the relations between the parameters $ a $, $ b $, $ p $, $ r $, $ s $ and $ t $. Some examples of such operators are also given.

Keywords

• fock space
• weighted composition operator
• 2-complex symmetric operator
• reproducing kernel function