Sampling theorems on locally compact groups from oscillation estimates

2005/09/08 by Hartmut Fuehr, Fuehr, Hartmut, Karlheinz Groechenig +1 · 1 citation
Mathematics · #26D10 #42B35 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 43A80 #Representation Theory (math.RT) #Secondary 42C40 #math.FA #math.RT #msc:26D10 #msc:42B35 #msc:42C40 #msc:43A80

paper · pdf · doi:10.48550/arxiv.math/0509178

18 pages

arxiv created 2005/09/08 · arxiv updated 2009/12/01

Abstract

We present a general approach to derive sampling theorems on locally compact groups from oscillation estimates. We focus on the \rm 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.

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• Frame redundancy and Beurling density

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