virtuell

A function of two variables and is called a Hardy kernel, if it is homogeneous of degree minus one: . Hardy kernels are usually associated with integral operators on the positive semi-axis. Because of the homogeneity of the kernel, such operators are easily diagonalisable by the Mellin transform, and so the spectral theory of this class of operators is very simple. In the talk, I will discuss spectral properties of matrices , obtained by restrictions of Hardy kernels onto integers. Of course, after restricting to integers, the homogeneity property ``disappears`` and it is no longer clear how to diagonalise such matrices. Nevertheless, it turns out that some progress can be made in their spectral analysis. I will state some general theorems and consider in detail some examples.

Alexander Pushnitski

King's College London