Hauptmenü
  • Autor
    • Aistleitner, Christoph
    • Berkes, István
    • Seip, Kristian
    • Weber, Michel
  • TitelConvergence of series of dilated functions and spectral norms of GCD matrices
  • Volltext
  • DOI10.4064/aa168-3-2
  • Erschienen inActa Arithmetica
  • Band168
  • Erscheinungsjahr2015
  • Heft3
  • Seiten221-246
  • LicenceCC BY
  • ISSN1730-6264
  • ZugriffsrechteCC-BY
  • Download Statistik14
  • Peer ReviewJa
  • AbstractIn the present paper we establish a connection between the L^2 norm of sums of dilated functions whose Fourier coefficients are of order O(j^{−α}) for some α ∈ (1/2, 1), and the spectral norms of certain greatest common divisor (GCD) matrices. Utilizing recent bounds for these spectral norms, we obtain necessary and sufficient conditions for the convergence in L^2 and for the almost everywhere convergence of series of dilated functions.