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On the spectrum of Volterra-type integral operators on Fock--Sobolev spaces (1612.06307v1)
Published 19 Dec 2016 in math.CV and math.FA
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.