Führ, Hartmut;Gröchenig, Karlheinz

Sampling theorems on locally compact groups from oscillation estimates

Math. Z. Vol.255 No.1 (2007) p.177-194, Zbl:1132.43005, MR2262727

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abstract

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