Wavelet Transforms and Admissible Group Representations

  • Eric Weber
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


Discrete wavelet transforms arise naturally from the sampling of a continuous wavelet transform, which in turn arises from a square-integrable (or more generally, admissible) representation of a locally compact group. We show that discrete wavelet transforms arising from groups with an affine structure possess an analogous admissibility condition. In particular, we show that the group performing the role of translations must satisfy an admissibility property. Finally, we relate these results to several notions of multiresolution.


Wavelet Transform Discrete Wavelet Multiresolution Analysis Regular Representation Frame Representation 
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Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Eric Weber
    • 1
  1. 1.Department of MathematicsIowa State UniversityAmes

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