Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SPECTRAL PROPERTIES OF VOLTERRA-TYPE INTEGRAL OPERATORS ON FOCK-SOBOLEV SPACES

  • Mengestie, Tesfa (Department of Mathematical Sciences Western Norway University of Applied Sciences)
  • Received : 2016.10.16
  • Accepted : 2017.02.27
  • Published : 2017.11.01
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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 ${\mathcal{F}}^p_{{\psi}m}$. 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.

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