- Autor
- Aistleitner, Christoph
- Berkes, István
- Seip, Kristian
- Weber, Michel
- TitelConvergence of series of dilated functions and spectral norms of GCD matrices
- Datei
- DOI10.4064/aa168-3-2
- Erschienen inActa Arithmetica
- Band168
- Erscheinungsjahr2015
- Heft3
- Seiten221-246
- LicenceCC BY
- ISSN1730-6264
- Download Statistik873
- 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.
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