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.
Categories: math.CV math.FA