[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j160671

SPECTRAL PROPERTIES OF VOLTERRA-TYPE INTEGRAL OPERATORS ON FOCK-SOBOLEV SPACES

Mengestie, Tesfa (Department of Mathematical Sciences Western Norway University of Applied Sciences)

Publication Information

Journal of the Korean Mathematical Society / v.54, no.6, 2017 , pp. 1801-1816 More about this Journal

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 ${\mathcal{F}}^p_{{\psi}m}$ . We showed that $V_g$ is bounded on ${\mathcal{F}}^p_{{\psi}m}$ 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.

Keywords

Fock space; Fock-Sobolov spaces; bounded; compact; Volterra integral; multiplication operators; Schatten class; spectrum; generalized Fock spaces;

Citations & Related Records

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