Righetti, Mattia, Sepulcre, Juan Matias, Vidal, Tomás
The converse of Bohr's equivalence theorem with Fourier exponents linearly independent over the rational numbers
Journal of Mathematical Analysis and Applications. 2022, 513(2): 126240. https://doi.org/10.1016/j.jmaa.2022.126240
URI: http://hdl.handle.net/10045/122928
DOI: 10.1016/j.jmaa.2022.126240
ISSN: 0022-247X (Print)
Abstract: 
Given two arbitrary almost periodic functions with Fourier exponents which are linearly independent over the rational numbers, 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 or Bohr-equivalent. This result represents the converse of Bohr's equivalence theorem for this particular case.
Keywords:Bohr equivalence theorem, Dirichlet series, Converse theorem, Almost periodic functions
Elsevier
info:eu-repo/semantics/article