Convergence of series of dilated functions and spectral norms of GCD matrices

Christoph Aistleitner, István Berkes, Kristian Seip, Michel Weber

Research output: Contribution to journalArticlepeer-review

Abstract

We establish a connection between the L2 norm of sums of dilated functions whose jth Fourier coefficients are 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 sharp conditions for the convergence in L2 and for the almost everywhere convergence of series of dilated functions.
Original languageEnglish
Pages (from-to)221-246
JournalActa Arithmetica
Volume168
DOIs
Publication statusPublished - 2015

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)

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