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Transforms associated to square integrable group representations. II: Examples. (English) Zbl 0601.22001
We give examples of integral transforms defined through square integrable group representations, described in the first paper of this series [J. Math. Phys. 26, 2473-2479 (1985; Zbl 0571.22021)]. We focus on the Weyl and $''ax+b''$ groups and study their relevance in physics and applied mathematics.

MSC:
22A10Analysis on general topological groups
22E70Applications of Lie groups to physics; explicit representations
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Full Text: Numdam EuDML
References:
[1] A. Grossmann , J. Morlet and T. Paul , Journ. Math. Phys. , t. 26 , 1985 , p. 2473 . MR 803788 | Zbl 0571.22021 · Zbl 0571.22021 · doi:10.1063/1.526761
[2] T. Paul , J. Math. Phys. , t. 25 , 1984 , p. 3252 . MR 761848
[3] P. Goupillaud , A. Grossmann and J. Morlet , Geoexploration , t. 23 , 1984 - 1985 , p. 85 .
[4] A. Grossmann and T. Paul , Wave functions on subgroups of the group of affine canonical transformations . In : Resonances. Models and Phenonema . S. Albeverio, L. S. Ferreira and L. Streit, editors. Springer , Lecture Notes in Physics , Vol. 211 , 1984 , p. 128 . MR 777335
[5] T. Paul , Affine coherent states and the radial Schrödinger equation I. Radial harmonic oscillator and hydrogen atom, II Large N limit and III Affine Wigner functions , preprints, Luminy . Submitted to Annals of I. H. P. [6] I.M. Gelfand and M.A. Naimark , Dokl-Akad-Navk SSSR , t. 55 , 1954 , p. 570 .
[6] E.W. Aslasken and J.R. Klauder , J. Math. Phys. , t. 9 , 1968 , p. 206 . Zbl 0162.58403 · Zbl 0162.58403 · doi:10.1063/1.1664570