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Sampling theorems on locally compact groups from oscillation estimates

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Abstract

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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Author notes

  1. K. Gröchenig

    Present address: Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090, Wien, Austria

Authors and Affiliations

  1. Institute of Biomathematics and Biometry, GSF National Research Center for Environment and Health, Ingolstädter Landstrasse1, 85764, Neuherberg, Germany

    H. Führ & K. Gröchenig

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  1. H. Führ
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  2. K. Gröchenig
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Correspondence to H. Führ.

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Führ, H., Gröchenig, K. Sampling theorems on locally compact groups from oscillation estimates. Math. Z. 255, 177–194 (2007). https://doi.org/10.1007/s00209-006-0019-x

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  • DOI: https://doi.org/10.1007/s00209-006-0019-x

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