Classic balayage of measures and subharmonic functions to a system of rays

TL;DR

This paper develops a method for sweeping measures and subharmonic functions on rays in the complex plane, aiding the analysis of entire functions' growth and zero distribution.

Contribution

It introduces a classic balayage technique for measures and subharmonic functions on rays, including infinite order cases, with applications to entire functions and exponential systems.

Findings

Balances measures and subharmonic functions on rays

Analyzes growth and zero distribution of entire functions

Includes survey sections and new theoretical results

Abstract

We construct and apply the classic balayage (sweeping out) of measures and subharmonic functions on closed system of rays in the complex plane with vertex at the origin, including measures and subharmonic functions and infinite order. The need for such a procedure occurs in the study of the behavior of entire and subharmonic functions on systems of rays. The results apply to the complete regularity of the growth of subharmonic and entire functions on a system of rays, the study of the distribution of zeros of entire functions of exponential type of class A, touches upon the incompleteness of exponential systems. The paper contains a survey character sections and new results.