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

Christoph Aistleitner, Istvan Berkes, Kristian Seip +1

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 n…