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

• Autorzy: Christoph Aistleitner , István Berkes , Kristian Seip , Michel Weber
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42B05: Fourier series and coefficients
• 26A45: Functions of bounded variation, generalizations
• 42A61: Probabilistic methods
• 42A20: Convergence and absolute convergence of Fourier and trigonometric series
• 15A18: Eigenvalues, singular values, and eigenvectors
• 11A05: Multiplicative structure; Euclidean algorithm; greatest common divisors
• 42A16: Fourier coefficients, Fourier series of functions with special properties, special Fourier series

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 168
• Numer: 3
• Strony: 221-246

Daty

wydano

2015

Twórcy

autor

Christoph Aistleitner

• Institute of Mathematics A, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria

autor

István Berkes

• Institute of Statistics, TU Graz, Kopernikusgasse 24/III, 8010 Graz, Austria

autor

Kristian Seip

• Department of Mathematical Sciences, Norwegian University of Science, and Technology (NTNU), NO-7491 Trondheim, Norway

autor

Michel Weber

• IRMA, 10 rue du Général Zimmer, 67084 Strasbourg Cedex, France

Identyfikatory

DOI

10.4064/aa168-3-2