Mathematische Zeitschrift

, Volume 255, Issue 1, pp 177–194

Sampling theorems on locally compact groups from oscillation estimates

Article

DOI: 10.1007/s00209-006-0019-x

Cite this article as:
Führ, H. & Gröchenig, K. Math. Z. (2007) 255: 177. doi:10.1007/s00209-006-0019-x

Abstract

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

Keywords

Stratified Lie groups Paley-Wiener space Sampling theorems Frames Discrete series representations 

Mathematics Subject Classification (2000)

Primary 43A80 Primary 42B35 Secondary 42C40 Secondary 26D10 

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Institute of Biomathematics and BiometryGSF National Research Center for Environment and HealthNeuherbergGermany
  2. 2.Fakultät für MathematikUniversität WienWienAustria

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