Weighted superposition operators on Fock spaces

TL;DR

This paper characterizes all pairs of entire functions that induce weighted superposition operators transforming one Fock space into another, and explores their boundedness, Lipschitz continuity, and compactness properties.

Contribution

It provides a complete characterization of weighted superposition operators on Fock spaces and analyzes their analytical properties.

Findings

Identifies all pairs of entire functions inducing such operators.

Shows Fock spaces do not support compact weighted superposition operators.

Describes boundedness and Lipschitz continuity conditions.

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.