The spectrum of Volterra operators on weighted spaces of entire functions

TL;DR

This paper studies the spectral properties of Volterra operators with entire function symbols on various weighted spaces of entire functions, including Banach and H"ormander algebras.

Contribution

It provides a comprehensive analysis of the spectrum of Volterra operators on different weighted spaces of entire functions, extending previous results to new function spaces.

Findings

Characterization of the spectrum of $V_g$ on $H_v^{infty}(C)$

Spectral analysis of $V_g$ on H"ormander algebras $A_p$ and $A^0_p$

Identification of conditions for spectral properties depending on the symbol $g$

Abstract

We investigate the spectrum of the Volterra operator $V_g$ with symbol an entire function $g$, when it acts on weighted Banach spaces $H_v^{\infty}(\mathbb{C})$ of entire functions with sup-norms and when it acts on H\"ormander algebras $A_p$ or $A^0_p$.