On sums and products of periodic functions

TL;DR

This paper investigates conditions under which arithmetic operations on periodic functions preserve their periodicity, especially when these functions are defined on different domains.

Contribution

It provides new criteria for when sums and products of periodic functions remain periodic, considering functions with possibly non-overlapping domains.

Findings

Identifies conditions for sum and product of periodic functions to be periodic

Extends understanding of periodicity preservation to functions with restricted domains

Offers theoretical insights into the structure of periodic functions

Abstract

The main purpose of this work is to ascertain when arithmetic operations with periodic functions whose domains may not coincide with the whole real line preserve periodicity.