1.Institute of Biomathematics and Biometry,GSF National Research Center for Environment and Health,Neuherberg,Germany;2.Fakult?t für Mathematik,Universit?t Wien,Wien,Austria
Abstract:
We present a general approach to derive sampling theorems on locally compact groups from oscillation estimates. We focus on the L2-stability of the sampling operator by using notions from frame theory. This approach yields particularly simple and transparent reconstruction procedures. We then apply these methods to the discretization of discrete series representations and to Paley–Wiener spaces on stratified Lie groups.