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arXiv · 1612.06307

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

Tesfa Mengestie
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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.

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Tesfa Mengestie. 2016-12-19. On the spectrum of Volterra-type integral operators on Fock--Sobolev spaces. https://arxiv.org/abs/1612.06307

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