Convergence of series of dilated functions and spectral norms of GCD matrices
Acta Arithmetica, Tome 168 (2015) no. 3, pp. 221-246
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We establish a connection between the $L^2$ norm of sums of dilated functions whose $j$th Fourier coefficients are $\mathcal {O}(j^{-\alpha })$ for some $\alpha \in (1/2,1)$, 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 $L^2$ and for the almost everywhere convergence of series of dilated functions.
Keywords:
establish connection between norm sums dilated functions whose jth fourier coefficients mathcal alpha alpha spectral norms certain greatest common divisor gcd matrices utilizing recent bounds these spectral norms obtain sharp conditions convergence almost everywhere convergence series dilated functions
Affiliations des auteurs :
Christoph Aistleitner 1 ; István Berkes 2 ; Kristian Seip 3 ; Michel Weber 4
@article{10_4064_aa168_3_2,
author = {Christoph Aistleitner and Istv\'an Berkes and Kristian Seip and Michel Weber},
title = {Convergence of series of dilated functions and spectral norms of {GCD} matrices},
journal = {Acta Arithmetica},
pages = {221--246},
publisher = {mathdoc},
volume = {168},
number = {3},
year = {2015},
doi = {10.4064/aa168-3-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa168-3-2/}
}
TY - JOUR AU - Christoph Aistleitner AU - István Berkes AU - Kristian Seip AU - Michel Weber TI - Convergence of series of dilated functions and spectral norms of GCD matrices JO - Acta Arithmetica PY - 2015 SP - 221 EP - 246 VL - 168 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/aa168-3-2/ DO - 10.4064/aa168-3-2 LA - en ID - 10_4064_aa168_3_2 ER -
%0 Journal Article %A Christoph Aistleitner %A István Berkes %A Kristian Seip %A Michel Weber %T Convergence of series of dilated functions and spectral norms of GCD matrices %J Acta Arithmetica %D 2015 %P 221-246 %V 168 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/aa168-3-2/ %R 10.4064/aa168-3-2 %G en %F 10_4064_aa168_3_2
Christoph Aistleitner; István Berkes; Kristian Seip; Michel Weber. Convergence of series of dilated functions and spectral norms of GCD matrices. Acta Arithmetica, Tome 168 (2015) no. 3, pp. 221-246. doi: 10.4064/aa168-3-2
Cité par Sources :