Volterra type operators on growth Fock spaces

TL;DR

This paper studies Volterra type and weighted composition operators on growth Fock spaces in complex Euclidean spaces, focusing on their properties and approximation techniques related to unbounded radial weights.

Contribution

It introduces new analysis of these operators on growth Fock spaces, utilizing approximation of weights by entire maps, which advances understanding of their structure and boundedness.

Findings

Characterization of operators on growth Fock spaces

Use of approximation techniques for unbounded weights

Insights into operator boundedness and structure

Abstract

Let $\omega$ be an unbounded radial weight on $\mathbb{C}^d$, $d\ge 1$. Using results related to approximation of $\omega$ by entire maps, we investigate Volterra type and weighted composition operators defined on the growth space $\mathcal{A}^\omega(\mathbb{C}^d)$. Special attention is given to the operators defined on the growth Fock spaces.