@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}, pages = {201--236}, publisher = {Gauthier-Villars}, volume = {59}, number = {2}, year = {1993}, mrnumber = {1277217}, zbl = {0923.43004}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1993__59_2_201_0/} }
TY - JOUR AU - Kalisa, C. AU - Torrésani, B. TI - N-dimensional affine Weyl-Heisenberg wavelets JO - Annales de l'I.H.P. Physique théorique PY - 1993 SP - 201 EP - 236 VL - 59 IS - 2 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1993__59_2_201_0/ LA - en ID - AIHPA_1993__59_2_201_0 ER -
Kalisa, C.; Torrésani, B. N-dimensional affine Weyl-Heisenberg wavelets. Annales de l'I.H.P. Physique théorique, Tome 59 (1993) no. 2, pp. 201-236. http://www.numdam.org/item/AIHPA_1993__59_2_201_0/
[Al.An.Ga.1] 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
, and ,[Al.An.Ga.2] 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
, and ,[Al.Go] Quantization, Coherent States and Diffeomorphisms Groups, Lect. Notes in Phys., Vol. 379, 1991, p. 147. | MR
and ,[As.Kl] J. Math. Phys., Vol. 10, 1969, p. 2267. | Zbl
and ,[Aus.Ko] Polarization and Unitary Representations of Solvable Lie Groups, Invent. Math., Vol. 14, 1971, pp. 255-354. | MR | Zbl
and ,[Bar] On Unitary Ray Representations for Continuous Groups, Ann. Math., Vol. 48, 1947, pp. 568-640. | MR | Zbl
,[Bo.Fo.Ro] Homogeneous Kahler Manifolds : Paving the Way Towards Supersymmetric Nonlinear Sigma Models, Comm. Math. Phys., Vol. 102, 1986, pp. 605-647. | MR | Zbl
, and ,[Cal] Intermediate Spaces and Interpolation, the Complex Method, Studia Math., Vol. 24, 1964, p. 113. | MR | Zbl
,[Car] Square-Integrable Representations of Non-Unimodular Groups, Bull. Austr. Math. Soc., Vol. 15, 1976, p. 1. | MR | Zbl
,[Da] S.I.A.M., 1992. | MR
, Ten Lectures on Wavelets,[Di] Les C*-algèbres et leurs représentations, Cahiers scientifiques, Vol. 29, Gauthier-Villars, 1957. | MR
,[DB] Coherent States Over Symplectic Homogeneous Spaces, J. Math. Phys., Vol. 30, 1989, pp. 1401-1407. | MR | Zbl
,[Du.Moo] On the Regular Representation of a Nonunimodular Locally Compact Group, J. Funct. An., Vol. 21, 1976, pp. 209- 243. | MR | Zbl
and ,[Fr.Ja.We] Littlewood-Paley Theory and the Classification of Function Spaces, NSF-CBMS Conf. Series, 1991.
, and ,[Ga] Theory of Communication, J. I.E.E., Vol. 903, 1946, pp. 429-457.
,[God] Sur les relations d'orthogonalité de V. Bargmann, C. R. Acad. Sci., Vol. 255, 1947, pp. 521-523, pp. 657-659. | Zbl
,[Gr.Mo] Decomposition of Hardy Functions Into Wavelets of Constant Shape, S.I.A.M., J. Math. An., Vol. 15, 1986. | Zbl
and ,[Gr.Mo.Pa.1] Transforms Associated to Square-Integrable Group Representations I, J. Math. Phys., Vol. 27, 1985, p. 2473. | Zbl
, and ,[Gr.Mo.Pa.2] Transforms Associated to Square-Integrable Group Representations II, Ann. Inst. H. Poincaré, Vol. 45, 1986, p. 293. | Numdam | Zbl
, and ,[Gui] Théorie de Mackey et méthode des orbites selon M. Duflo, Expo. Math., Vol. 3, 1985, pp. 303-346. | MR | Zbl
,[He.Wa] Continuous and Discrete Wavelet Transforms, S.I.A.M. Reviews, Vol. 31, 1989, p. 628. | MR | Zbl
and ,[Ka] Ondelettes canoniques, galiléennes et relativistes multidimensionnelles, Ph. D. Thesis, Louvain-la-Neuve, 1992.
,[Kir] Éléments de théorie des représentations, Mir, Moscou, 1974.
,[Kl.Sk] Coherent States-Applications in Physics and Mathematical Physics, World Scientific, 1985. | MR | Zbl
and ,[Mac] Theory of Unitary Group Representations, University of Chicago Press, 1976. | MR | Zbl
,[Me.1] Ondelettes et applications, CEREMADE, Preprint, 1991.
,[Me.2] Ondelettes et opérateurs I: ondelettes, Hermann, 1989. | MR | Zbl
,[Mo] Coherent States Representations of Nilpotent Lie Groups, Comm. Math. Phys., Vol. 54, 1977, pp. 63-68. | MR | Zbl
,[Mo.Ve] Coherent States and Square-Integrable Representations, Ann. I.H.P., Physique Théorique, Vol. 39, 1978, pp. 139-156. | Numdam | MR | Zbl
and ,[Mu] Ondelettes multidimensionnelles et application à l'analyse d'images, Ph. D. Thesis, Louvain-la-Neuve, 1990.
,[Pe] Generalized Coherent States and Their Applications, Springer, Berlin, 1986. | MR | Zbl
,[Pu] Leçons sur les représentations des groupes, Dunod, 1966. | MR
,[Sch] Harmonic Analysis on the Heisenberg Nilpotent Lie Group, Pitman Series, Wiley, Vol. 147, 1986.
,[To.1] Wavelets Associated With Representations of the Affine Weyl-Heisenberg Group, J. Math. Phys., Vol. 32, 1991, pp. 1273-1279. | MR | Zbl
,[To.2] Time-Frequency Representations: Wavelet Packets and Optimal Decomposition, Ann. Inst. H. Poincaré, Phys. Th.,, Vol. 56, 1992, pp. 215-234. | Numdam | MR | Zbl
,[Vil] Special Functions and Theory of Group Representations, A.M.S., Providence, 1968.
,[Wi]
, I.N.R.I.A. Lectures on Wavelet Packets Algorithms, Yale University preprint, 1990.