Poincaré Coherent States and Relativistic Phase Space Analysis
Part of the inverse problems and theoretical imaging book series (IPTI)
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 , which have been thoroughly discussed during this colloquium:
the affine (ax+b) group, which yields the usual wavelet analysis;
the Weyl-Heisenberg group, which leads to various phase space or time- frequency representations.
Unable to display preview. Download preview PDF.
- 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
- A. Borei, Représentations des Groupes Localement Compacts, Lect. Notes in Mathematics, vol. 276, Springer, Berlin et al. 1972Google Scholar
© Springer-Verlag Berlin Heidelberg 1990