Sampling Almost Periodic and Related Functions

  • Stefano Ferri
  • Jorge GalindoEmail author
  • Camilo Gómez


We consider certain finite sets of circle-valued functions defined on intervals of real numbers and estimate how large the intervals must be for the values of these functions to be uniformly distributed in an approximate way. This is used to establish some general conditions under which a random construction introduced by Katznelson for the integers yields sets that are dense in the Bohr group. We obtain in this way very sparse sets of real numbers (and of integers) on which two different almost periodic functions cannot agree, which makes them amenable to be used in sampling theorems for these functions. These sets can be made as sparse as to have zero asymptotic density or as to be t-sets, i.e., to be sets that intersect any of their translates in a bounded set. Many of these results are proved not only for almost periodic functions but also for classes of functions generated by more general complex exponential functions, including chirps or polynomial phase functions.


Almost periodic function Bohr topology Matching set Sampling set Chirp Polynomial phase functions Discrepancy Uniform distribution Sampling T-set Bohr-dense 

Mathematics Subject Classification

Primary 43A60 Secondary 11K70 42A75 94A20 



We would like to thank the anonymous referees for the appreciable number of corrections and improvements they suggested. We truly believe their input has resulted in a better paper.


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Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad de los AndesBogotá D.C.Colombia
  2. 2.Instituto Universitario de Matemáticas y Aplicaciones (IMAC)Universidad Jaume ICastellónSpain
  3. 3.Facultad de IngenieríaUniversidad de La Sabana, Campus Universitario Puente del ComúnChíaColombia
  4. 4.Departamento de MatemáticasEscuela Colombiana de IngenieríaBogotá D.C.Colombia

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