BALAYAGE ON A SYSTEM OF RAYS AND ENTIRE-FUNCTIONS OF COMPLETELY REGULAR GROWTH

This paper presents a technique for constructing functions that are subharmonic in the complex plane, agree with a given subharmonic function u on a system S of rays with vertex at the origin, and are harmonic outside S. For a wide class of systems S, this technique permits one to obtain criteria for the complete regularity of growth of entire functions f on S in terms of the balayage of the distribution of zeros of f.