Meromorphic almost periodic functions

TL;DR

This paper investigates meromorphic functions that are almost periodic in a strip, providing a comprehensive description of their zeros and poles, and establishing conditions for their sums, products, and quotients to also be almost periodic.

Contribution

It offers a complete characterization of zeros and poles for meromorphic almost periodic functions and conditions for their algebraic operations to preserve almost periodicity.

Findings

Complete description of zeros and poles for meromorphic almost periodic functions

Conditions for quotients of holomorphic almost periodic functions

Necessary and sufficient conditions for sums and products to be almost periodic

Abstract

We study meromorphic functions in a strip almost periodic with respect to the spherical metric. Then we get a complete description of zeros and poles for this class of functions, find a condition for a meromorphic almost periodic function to be a quotient of two holomorphic almost periodic function, find a necessary and suficient condition for sum and product of almost periodic meromorphic functions to be almost periodic.