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

Christoph Aistleitner; István Berkes; Kristian Seip; Michel Weber

Acta Arithmetica (2015)

- Volume: 168, Issue: 3, page 221-246
- ISSN: 0065-1036

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topChristoph 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 -

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