@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 -
