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  • Autor
    • Bazarova, Alina
    • Berkes, István
    • Raseta, Marko
  • TitelStrong approximation of lacunary series with random gaps
  • Volltext
  • DOI10.1007/s00605-017-1059-5
  • Erschienen inMonatshefte für Mathematik
  • Erscheinungsjahr2017
  • LicenceCC BY
  • ISSN1436-5081
  • ZugriffsrechteCC-BY
  • Download Statistik54
  • Peer ReviewNein
  • AbstractWe investigate the asymptotic behavior of sums \(Σ^N_{k=1} f (n_k x)\), where f is a mean zero, smooth periodic function on \(\mathbb{R}\) and \((n_k )_{k≥1}\) is a random sequence such that the gaps \(n_{k+1} − n_k\) are i.i.d. Our result shows that, in contrast to the classical Salem-Zygmund theory, the almost sure behavior of lacunary series with random gaps can be described very precisely without any assumption on the size of the gaps.