On the Spectrum of Volterra-Type Integral Operators on Fock–Sobolev Spaces

We determine the spectrum of the Voltterra-type integral operators Vg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_g$$\end{document} on the growth type Fock–Sobolev spaces Fψm∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {F}_{\psi _m}^\infty $$\end{document}. 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.