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

Christoph Aistleitner, et al. "Convergence of series of dilated functions and spectral norms of GCD matrices." Acta Arithmetica 168.3 (2015): 221-246. <http://eudml.org/doc/279198>.

@article{ChristophAistleitner2015,
abstract = {We establish a connection between the L² norm of sums of dilated functions whose jth Fourier coefficients are $(j^\{-α\})$ 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.},
author = {Christoph Aistleitner, István Berkes, Kristian Seip, Michel Weber},
journal = {Acta Arithmetica},
keywords = {function series; dilated functions; Fourier coefficients; almost everywhere convergence; GCD matrices; probabilistic methods},
language = {eng},
number = {3},
pages = {221-246},
title = {Convergence of series of dilated functions and spectral norms of GCD matrices},
url = {http://eudml.org/doc/279198},
volume = {168},
year = {2015},
}

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
VL - 168
IS - 3
SP - 221
EP - 246
AB - We establish a connection between the L² norm of sums of dilated functions whose jth Fourier coefficients are $(j^{-α})$ 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.
LA - eng
KW - function series; dilated functions; Fourier coefficients; almost everywhere convergence; GCD matrices; probabilistic methods
UR - http://eudml.org/doc/279198
ER -