A class of completely continuous operators in a Hilbert space of entire functions of exponential type

Abstract

Any positive Borel measureμ in Rn which satisfies the conditionsup μ{x∈Rn¦ ¦x−y¦≤1}<∞ generates a Hermitian bilinear form in the Hilbert space of entire functionsf: Cn→C1 of exponential type not exceedingτ which are square-summable on Rn. In this paper a criterion is given for the complete continuity of this form.