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Sampling theorems on locally compact groups from oscillation estimates

Research paper by Hartmut Fuehr, Karlheinz Groechenig

Indexed on: 08 Sep '05Published on: 08 Sep '05Published in: Mathematics - Functional Analysis



Abstract

We present a general approach to derive sampling theorems on locally compact groups from oscillation estimates. We focus on the ${\rm L}^2$-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.