A generalization of Bohr's Equivalence Theorem

TL;DR

This paper extends Bohr's equivalence theorem to a broader class of almost periodic functions via a generalized equivalence relation for Dirichlet series, analyzing their value sets within their strips of almost periodicity.

Contribution

It introduces a generalized equivalence relation for Dirichlet series and extends Bohr's theorem to almost periodic functions, broadening the theoretical framework.

Findings

Extended Bohr's equivalence theorem to new classes of functions

Characterized the value sets of equivalent almost periodic functions

Provided a unified approach to Dirichlet series and almost periodic functions

Abstract

Based on a generalization of Bohr's equivalence relation for general Dirichlet series, in this paper we study the sets of values taken by certain classes of equivalent almost periodic functions in their strips of almost periodicity. In fact, the main result of this paper consists of a result like Bohr's equivalence theorem extended to the case of these functions.