On the spectrum of Volterra-type integral operators on Fock--Sobolev spaces

TL;DR

This paper characterizes the spectrum, boundedness, and compactness of Volterra-type integral operators on Fock--Sobolev spaces, linking operator properties to the function-theoretic features of the inducing map g.

Contribution

It provides a complete spectral characterization of Volterra-type operators on Fock--Sobolev spaces and relates their properties to the inducing function g.

Findings

Spectrum of V_g determined on Fock--Sobolev spaces

Boundedness and compactness characterized by properties of g

Spaces described via Littlewood--Paley formula

Abstract

We determine the spectrum of the Voltterra-type integral operators $V_g$ on the growth type Fock--Sobolev spaces $\mathcal{F}_{\psi_m}^\infty$. We also characterized the bounded and compact spectral properties of the operators in terms of function-theoretic properties of the inducing map $g$. As a means to prove our main results, we first described the spaces in terms of Littlewood--Paley type formula which is interest of its own.