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arXiv · 1407.5403

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

Christoph Aistleitner·Istvan Berkes·Kristian Seip·Michel Weber
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Abstract

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.

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Christoph Aistleitner, Istvan Berkes, Kristian Seip, Michel Weber. 2014-07-21. Convergence of series of dilated functions and spectral norms of GCD matrices. https://arxiv.org/abs/1407.5403

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