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arXiv · 1702.08157

Spectral properties of Volterra-type integral operators on Fock--Sobolev spaces

Tesfa Mengestie
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Abstract

We study some spectral properties of Volterra-type integral operators $V_g$ and $I_g$ with holomorphic symbol $g$ on the Fock--Sobolev spaces $\mathcal{F}_{\psi_m}^p$. We showed that $V_g$ is bounded on $\mathcal{F}_{\psi_m}^p$ if and only if $g$ is a complex polynomial of degree not exceeding two, while compactness of $V_g$ is described by degree of $g$ being not bigger than one. We also identified all those positive numbers $p$ for which the operator $V_g$ belongs to the Schatten $\mathcal{S}_p$ classes. Finally, we characterize the spectrum of $V_g$ in terms of a closed disk of radius twice the coefficient of the highest degree term in a polynomial expansion of $g$.

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Tesfa Mengestie. 2017-02-27. Spectral properties of Volterra-type integral operators on Fock--Sobolev spaces. https://arxiv.org/abs/1702.08157

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