To the Liouville theorem for entire functions of finite order

TL;DR

This paper provides a concise, independent proof of a Liouville-type theorem for entire and subharmonic functions of finite order, extending classical results to functions bounded outside negligible sets.

Contribution

It introduces a novel, simplified proof of the Liouville theorem for functions of finite order, applicable outside sets of zero planar density.

Findings

Proof is shorter and more independent than previous ones

Extends Liouville theorem to functions bounded outside zero density sets

Applicable to entire and subharmonic functions of finite order

Abstract

We present a new, short and independent proof of the Liouville-type theorem for entire and subharmonic functions of finite order bounded outside some set of zero planar density.