Sampling theorems on locally compact groups from oscillation estimates

Details Sampling theorems on locally compact groups from oscillation estimates Sampling theorems on locally compact groups from oscillation estimates

2005-09-08

arxiv.org/abs/math/0509178v1

Mathematics

Functional Analysis

18 pages

Scientific paper

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.

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