Weighted superposition operators on Fock spaces

Abstract: We characterize all pairs of entire functions $(u,\psi)$ for which the induced weighted superposition operator $S_{(u,\psi)}$ transforms one Fock space into another Fock space.Further analytical structures like boundedness and Lipschitz continuity of $S_{(u,\psi)}$ are described. We, in particular, show the Fock spaces support no compact weighted superposition operator.