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

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-psi m(p). We showed that V-g is bounded on 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 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.