Wavelets pp 221-231 | Cite as

Poincaré Coherent States and Relativistic Phase Space Analysis

  • J.-P. Antoine
Conference paper
Part of the inverse problems and theoretical imaging book series (IPTI)

Abstract

Group theory is one of the cornerstones of wavelet analysis. Indeed, at a very general level, one may say that the following three concepts are equivalent: (i) a square integrable representation U of a group G; (ii) coherent states over G; (iii) the wavelet transform associated to U.This analysis is familiar in the two standard cases [1], which have been thoroughly discussed during this colloquium:
  1. (i)

    the affine (ax+b) group, which yields the usual wavelet analysis;

     
  2. (ii)

    the Weyl-Heisenberg group, which leads to various phase space or time- frequency representations.

     

Keywords

Stein Acoustics 

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References

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    S.T. Ali and J.-P. Antoine, Coherent states of the 1+1 dimensional Poincaré group: square integrability and a relativistic Weyl transform, preprint UCL-IPT-87-39Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • J.-P. Antoine
    • 1
  1. 1.Institut de Physique ThéoriqueUniversité Catholique de LouvainLouvain-la-NeuveBelgium

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