A class of functional equations associated with almost periodic functions

Abstract

In this paper we will get a class of functional equations involving a countable set of terms, summed by the well known Bochner–Fejér summation procedure, which are closely associated with the set of almost periodic functions. We will show that the zeros of a prefixed almost periodic function determine analytic solutions of such a functional equation associated with it, and we will obtain other solutions which are analytic or meromorphic on a certain domain.

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Correspondence to J. M. Sepulcre.

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J. M. Sepulcre was supported by PGC2018-097960-B-C22 (MCIU/AEI/ERDF, UE).

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Sepulcre, J.M., Vidal, T. A class of functional equations associated with almost periodic functions. Aequat. Math. (2020). https://doi.org/10.1007/s00010-020-00732-3

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Keywords

  • Almost periodic functions
  • Dirichlet series
  • Bochner–Fejér summation method
  • Zeros of analytic functions
  • Functional equations

Mathematics Subject Classification

  • 42A75
  • 30D05
  • 39B32
  • 39Bxx
  • 30Axx