A Generalization of Bohr’s Equivalence Theorem

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 classes of functions that are associated with countable sets of distinct real numbers having an integral basis.