Weighted composition operators on weighted Fock spaces

We provide a complete characterization of the bounded, compact, and Hilbert-Schmidt class weighted composition operators acting on weighted Fock spaces, extending the classical Fock space characterization due to Le [11].

An estimate for the essential norm of these operators is also provided.

Our approach relies on the asymptotic behavior of the Mittag-Leffler function.

As applications, we establish explicit criteria for weighted composition operators with exponential weights and recover corresponding results for composition operators.