Zero (sub)sets for spaces of holomorphic functions and (sub)harmonic minorants

TL;DR

This paper establishes general conditions involving balayage and Green's functions that determine when a sequence of points can serve as the zero set for weighted holomorphic function spaces in complex domains.

Contribution

It introduces new criteria based on balayage and Green's functions for identifying zero sets in weighted holomorphic spaces.

Findings

Derived conditions for zero sets using balayage and Green's functions.

Applicable to various weighted spaces of holomorphic functions.

Provides a framework for understanding zero distributions in complex analysis.

Abstract

We obtain various general conditions in terms of the balayage and Green's functions under which the sequence of points is the zero set for weighted spaces of holomorphic functions in a domain on the complex plane.