Sets of values of equivalent almost periodic functions

TL;DR

This paper introduces a new equivalence relation for almost periodic functions, extending Bohr's theorem to a broader class of these functions, thereby advancing the theoretical understanding of their properties.

Contribution

It proposes a novel equivalence relation on almost periodic functions and extends Bohr's equivalence theorem to encompass all such functions.

Findings

Established a new equivalence relation for almost periodic functions

Extended Bohr's equivalence theorem to all almost periodic functions

Provided theoretical foundations for further analysis of these functions

Abstract

In this paper we establish a new equivalence relation on the spaces of almost periodic functions which allows us to prove a result like Bohr's equivalence theorem extended to the case of all these functions.