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

Any positive Borel measure $\mu$ in $R^n$ which satisfies the condition $\sup\limits_y\mu\{x\in R^n\mid|x-y|\le1\}<\infty$ generates a Hermitian bilinear form in the Hilbert space of entire functions $f\colon C^n\to C^1$ of exponential type not exceedingtau which are square-summable on $R^n$. In this paper a criterion is given for the complete continuity of this form.