L² interpolation and sampling

DrorVarolin
UI Urbana-Champaign, USA

Abstract

Let X  be an open Riemann surface. We consider the problem of interpolating or sampling values, along a sequence of points, of functions lying in a generalized Bergman space on X. The results are analogous to those of Seip-Wallsten and Berndtsson-Ortega: we define densities associated to the sequence, and show that if the sequence remains below a critical density then it is an interpolatios sequence, while if it exceeds a critical density then it is a sampling sequence. This is joint work with Alex Schuster.