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

We determine the spectrum of the Voltterra-type integral operators $V_g$ on the growth type Fock–Sobolev spaces ${\mathcal{F}}_{{\psi }_m}^{\mathrm{\infty }}$. 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.