The spectrum of some Hardy kernel matrices

Ole Fredrik Brevig, Karl-Mikael Perfekt, Alexander Pushnitski

For $\alpha >0$ we consider the operator $K_{\alpha }:{\ell }^2\to {\ell }^2$ corresponding to the matrix \[\left(\frac{(nm)^{-\frac{1}{2}+α}}{[\max(n,m)]^{2α}}\right)_{n,m=1}^\infty.\] By int…