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

2017/02/27 by Tesfa Mengestie, Mengestie, Tesfa · 1 citation
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1702.08157

openalex publication_date 2017/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 F_ψm^p. We showed that V_g is bounded on F_ψm^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 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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