The equivalence principle for almost periodic functions

M. Righetti, J. M. Sepulcre, T. Vidal

Published 2019-01-22Version 1

Given two arbitrary almost periodic functions, we prove that the existence of a common open vertical strip $V$, where both functions assume the same set of values on every open vertical substrip included in $V$, is a necessary and sufficient condition for both functions to have the same region of almost periodicity and to be $^*$-equivalent. This represents an improvement of previous results and it settles the problem of Bohr's equivalence theorem not having a converse.