Convergence of series of dilated functions and spectral norms of GCD matrices
Christoph Aistleitner ; István Berkes ; Kristian Seip ; Michel Weber
Acta Arithmetica, Tome 168 (2015), p. 221-246 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:279198 
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     title = {Convergence of series of dilated functions and spectral norms of GCD matrices},
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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) pp. 221-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa168-3-2/