The converse of Bohr's equivalence theorem with Fourier exponents linearly independent over the rational numbers

2019/01/22 by M. Righetti, Righetti, M., J. M. Sepulcre +3
Computer Science · Mathematics · #11J72 #11K60 #30D20 #42A75 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #Digital Filter Design and Implementation #FOS: Mathematics #Mathematical Analysis and Transform Methods #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1901.07917

openalex publication_date 2019/01/22 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28

Abstract

Given two arbitrary almost periodic functions with associated 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.

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