N-dimensional affine Weyl-Heisenberg wavelets
Kalisa, C. ; Torrésani, B.
Annales de l'I.H.P. Physique théorique, Tome 59 (1993), p. 201-236 / Harvested from Numdam
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@article{AIHPA_1993__59_2_201_0,
     author = {Kalisa, C. and Torr\'esani, B.},
     title = {N-dimensional affine Weyl-Heisenberg wavelets},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {59},
     year = {1993},
     pages = {201-236},
     mrnumber = {1277217},
     zbl = {0923.43004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1993__59_2_201_0}
}

Kalisa, C.; Torrésani, B. N-dimensional affine Weyl-Heisenberg wavelets. Annales de l'I.H.P. Physique théorique, Tome 59 (1993) pp. 201-236. http://gdmltest.u-ga.fr/item/AIHPA_1993__59_2_201_0/

[Al.An.Ga.1] S.T. Ali, J.P. Antoine and J.P. Gazeau, Square-Integrability of Group Representations in Homogeneous Spaces I, Reproducing Triples and Frames, Ann. Inst. H. Poincaré, Vol. 55, 1991, pp. 829-856. | Numdam | Zbl 0752.22002

[Al.An.Ga.2] S.T. Ali, J.P. Antoine and J.P. Gazeau, Square-Integrability of Group Representations on Homogeneous Spaces II, Generalized Square-Integrability and Equivalent Families of Coherent States, Ann. Inst. H. Poincaré, Vol. 55, 1991, pp. 860-890. | Numdam | Zbl 0752.22003

[Al.Go] S.T. Ali and G.A. Goldin, Quantization, Coherent States and Diffeomorphisms Groups, Lect. Notes in Phys., Vol. 379, 1991, p. 147. | MR 1180088

[As.Kl] E.W. Aslasken and J.R. Klauder, J. Math. Phys., Vol. 10, 1969, p. 2267. | Zbl 0184.54601

[Aus.Ko] L. Auslander and B. Kostant, Polarization and Unitary Representations of Solvable Lie Groups, Invent. Math., Vol. 14, 1971, pp. 255-354. | MR 293012 | Zbl 0233.22005

[Bar] V. Bargmann, On Unitary Ray Representations for Continuous Groups, Ann. Math., Vol. 48, 1947, pp. 568-640. | MR 21942 | Zbl 0045.38801

[Bo.Fo.Ro] M. Bordemann, M. Forger and H. Romer, Homogeneous Kahler Manifolds : Paving the Way Towards Supersymmetric Nonlinear Sigma Models, Comm. Math. Phys., Vol. 102, 1986, pp. 605-647. | MR 824094 | Zbl 0585.53018

[Cal] A. Calderón, Intermediate Spaces and Interpolation, the Complex Method, Studia Math., Vol. 24, 1964, p. 113. | MR 167830 | Zbl 0204.13703

[Car] A.L. Carey, Square-Integrable Representations of Non-Unimodular Groups, Bull. Austr. Math. Soc., Vol. 15, 1976, p. 1. | MR 430146 | Zbl 0327.22008

[Da] I. Daubechies, Ten Lectures on Wavelets, S.I.A.M., 1992. | MR 1162107

[Di] J. Dixmier, Les C*-algèbres et leurs représentations, Cahiers scientifiques, Vol. 29, Gauthier-Villars, 1957. | MR 171173

[DB] S. De Bièvre, Coherent States Over Symplectic Homogeneous Spaces, J. Math. Phys., Vol. 30, 1989, pp. 1401-1407. | MR 1002242 | Zbl 0686.46049

[Du.Moo] M. Duflo and C.C. Moore, On the Regular Representation of a Nonunimodular Locally Compact Group, J. Funct. An., Vol. 21, 1976, pp. 209- 243. | MR 393335 | Zbl 0317.43013

[Fr.Ja.We] M. Frazier, B. Jawerth and G. Weiss, Littlewood-Paley Theory and the Classification of Function Spaces, NSF-CBMS Conf. Series, 1991.

[Ga] D. Gabor, Theory of Communication, J. I.E.E., Vol. 903, 1946, pp. 429-457.

[God] R. Godement, Sur les relations d'orthogonalité de V. Bargmann, C. R. Acad. Sci., Vol. 255, 1947, pp. 521-523, pp. 657-659. | Zbl 0029.19907

[Gr.Mo] A. Grossmann and J. Morlet, Decomposition of Hardy Functions Into Wavelets of Constant Shape, S.I.A.M., J. Math. An., Vol. 15, 1986. | Zbl 0578.42007

[Gr.Mo.Pa.1] A. Grossmann, J. Morlet and T. Paul, Transforms Associated to Square-Integrable Group Representations I, J. Math. Phys., Vol. 27, 1985, p. 2473. | Zbl 0571.22021

[Gr.Mo.Pa.2] A. Grossmann, J. Morlet and T. Paul, Transforms Associated to Square-Integrable Group Representations II, Ann. Inst. H. Poincaré, Vol. 45, 1986, p. 293. | Numdam | Zbl 0601.22001

[Gui] A. Guichardet, Théorie de Mackey et méthode des orbites selon M. Duflo, Expo. Math., Vol. 3, 1985, pp. 303-346. | MR 844414 | Zbl 0582.22010

[He.Wa] C. Heil and D. Walnut, Continuous and Discrete Wavelet Transforms, S.I.A.M. Reviews, Vol. 31, 1989, p. 628. | MR 1025485 | Zbl 0683.42031

[Ka] C. Kalisa, Ondelettes canoniques, galiléennes et relativistes multidimensionnelles, Ph. D. Thesis, Louvain-la-Neuve, 1992.

[Kir] A. Kirillov, Éléments de théorie des représentations, Mir, Moscou, 1974.

[Kl.Sk] J.R. Klauder and B.S. Skagerstam, Coherent States-Applications in Physics and Mathematical Physics, World Scientific, 1985. | MR 826247 | Zbl 1050.81558

[Mac] G. Mackey, Theory of Unitary Group Representations, University of Chicago Press, 1976. | MR 396826 | Zbl 0344.22002

[Me.1] Y. Meyer, Ondelettes et applications, CEREMADE, Preprint, 1991.

[Me.2] Y. Meyer, Ondelettes et opérateurs I: ondelettes, Hermann, 1989. | MR 1085487 | Zbl 0694.41037

[Mo] H. Moscovici, Coherent States Representations of Nilpotent Lie Groups, Comm. Math. Phys., Vol. 54, 1977, pp. 63-68. | MR 442152 | Zbl 0407.22011

[Mo.Ve] H. Moscovici and A. Verona, Coherent States and Square-Integrable Representations, Ann. I.H.P., Physique Théorique, Vol. 39, 1978, pp. 139-156. | Numdam | MR 513686 | Zbl 0392.22008

[Mu] R. Murenzi, Ondelettes multidimensionnelles et application à l'analyse d'images, Ph. D. Thesis, Louvain-la-Neuve, 1990.

[Pe] A.M. Perelomov, Generalized Coherent States and Their Applications, Springer, Berlin, 1986. | MR 899736 | Zbl 0605.22013

[Pu] L. Pukanszky, Leçons sur les représentations des groupes, Dunod, 1966. | MR 217220

[Sch] W. Schempp, Harmonic Analysis on the Heisenberg Nilpotent Lie Group, Pitman Series, Wiley, Vol. 147, 1986.

[To.1] B. Torrésani, Wavelets Associated With Representations of the Affine Weyl-Heisenberg Group, J. Math. Phys., Vol. 32, 1991, pp. 1273-1279. | MR 1103481 | Zbl 0748.46046

[To.2] B. Torrésani, Time-Frequency Representations: Wavelet Packets and Optimal Decomposition, Ann. Inst. H. Poincaré, Phys. Th.,, Vol. 56, 1992, pp. 215-234. | Numdam | MR 1155278 | Zbl 0760.42021

[Vil] M. Vilenkin, Special Functions and Theory of Group Representations, A.M.S., Providence, 1968.

[Wi] M.V. Wickerhauser, I.N.R.I.A. Lectures on Wavelet Packets Algorithms, Yale University preprint, 1990.