Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames
Annales de l'I.H.P. Physique théorique, Tome 55 (1991) no. 4, pp. 829-855.
partie suivante Square integrability of group representations on homogeneous spaces. II. Coherent and quasi-coherent states. The case of the Poincaré group 
@article{AIHPA_1991__55_4_829_0,
     author = {Ali, S. T. and Antoine, J.-P. and Gazeau, J.-P.},
     title = {Square integrability of group representations on homogeneous spaces. {I.} {Reproducing} triples and frames},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {829--855},
     publisher = {Gauthier-Villars},
     volume = {55},
     number = {4},
     year = {1991},
     mrnumber = {1144104},
     zbl = {0752.22002},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1991__55_4_829_0/}
}
TY  - JOUR
AU  - Ali, S. T.
AU  - Antoine, J.-P.
AU  - Gazeau, J.-P.
TI  - Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1991
SP  - 829
EP  - 855
VL  - 55
IS  - 4
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPA_1991__55_4_829_0/
LA  - en
ID  - AIHPA_1991__55_4_829_0
ER  - 
%0 Journal Article
%A Ali, S. T.
%A Antoine, J.-P.
%A Gazeau, J.-P.
%T Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames
%J Annales de l'I.H.P. Physique théorique
%D 1991
%P 829-855
%V 55
%N 4
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPA_1991__55_4_829_0/
%G en
%F AIHPA_1991__55_4_829_0
Ali, S. T.; Antoine, J.-P.; Gazeau, J.-P. Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames. Annales de l'I.H.P. Physique théorique, Tome 55 (1991) no. 4, pp. 829-855. http://archive.numdam.org/item/AIHPA_1991__55_4_829_0/

[1] S.T. Ali and J.-P. Antoine, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 51, 1989, p. 23. | Numdam | MR | Zbl

[2] S.T. Ali, J.-P. Antoine and J.-P. Gazeau, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 52, 1990, p. 83. | Numdam | MR | Zbl

[3] A. Perelomov, Generalized Coherent States and their Applications, Springer-Verlag, Berlin, 1986. | MR | Zbl

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

[5] S.T. Ali, Rivista Nuovo Cim, Vol. 8, #11, 1985, pp. 1-128. | MR

[6] S.T. Ali and E. Prugovecki, Acta Appl. Math., Vol. 6, 1986, p. 1. | MR | Zbl

[7] S.T. Ali and E. Prugovecki, Acta Appl. Math., Vol. 6, 1986, p. 19. | MR | Zbl

[8] S.T. Ali and E. Prugovecki, Acta Appl. Math., Vol. 6, 1986, p. 47. | MR | Zbl

[9] A. Grossmann and J. Morlet, S.I.A.M. J. Math. Anal., Vol. 15, 1984, p. 723. | MR | Zbl

[10] R.J. Duffin and A.C. Schaeffer, Trans. Am. Math. Soc., Vol. 72, 1952, p. 341. | MR | Zbl

[11] I. Daubechies, A. Grossmann and Y. Meyer, J. Math. Phys., Vol. 27, 1986, p. 1271. | MR | Zbl

[12] I. Daubechies, I.E.E.E. Trans. Inform. Theory, Vol. 36, 1990, p. 961. | MR | Zbl

[13] Y. Meyer, Ondelettes et Opérateurs I, II, Hermann, Paris, 1990. | MR | Zbl

[14] J.-M. COMBES, A. GROSSMANN and P. TCHAMITCHIAN Eds., Wavelets: Time-Frequency Methods and Phase Space, Proc. Marseille, 1987, Springer-Verlag, Berlin, 1989. | MR | Zbl

[15] C.E. Heil and D.F. Walnut, S.I.A.M. Review, Vol. 31, 1989, p. 628. | MR | Zbl

[16] S.T. Ali, J.-P. Antoine and J.-P. Gazeau, Square Integrability of Group Representations on Homogeneous Spaces. II. Coherent and Quasi-Coherent states - The Case of the Poincaré Group, Ann. Inst. H. Poincaré, Phys. Theor., Vol. 55, 1991, p. 857- 890. | Numdam | MR | Zbl

[17] S.K. Berberian, Notes on Spectral Theory, Van Nostrand, Princeton, N.J., 1966. | MR | Zbl

[18] M. Takesaki, Theory of Operator Algebras I, Springer-Verlag, Berlin, 1979, Chap. IV, Sec. 8. | Zbl

[19] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien (Algèbres de von Neumann), Gauthier-Villars, Paris, 1957, 1969. | Zbl

[20] M.A. Naimark, Am. Math. Soc. Trans. Ser. 2, Vol. 5, 1975, p. 35.

[21] H. Meschkowsky, Hilbertsche Räume mit Kernfunction, Springer-Verlag, Berlin, 1962. | Zbl

[22] S.T. Ali, J.-P. Antoine and J.-P. Gazeau, Continuous Frames in Hilbert Space (in preparation). | Zbl

[23] A. Grossmann, J. Morlet and T. Paul, J. Math. Phys., Vol. 26, 1985, p. 2473; Ann. Inst. H. Poincaré, Phys. Théor., Vol. 45, 1986, p. 293. | Numdam | MR | Zbl

[24] M. Holschneider and Ph. Tchamitchian, Invent. Math., Vol. 105, 1991, p. 157. M. Holschneider, Inverse Radon Transforms Through Inverse Wavelet Transforms, Inverse Problems (to appear). | MR | Zbl

[25] S. De Bièvre, J. Math. Phys., Vol. 30, 1989, p. 1401. | Zbl

[26] S.T. Ali and G.A. Goldin, Quantization, Coherent States and Diffeomorphism Groups, in Differential Geometry, Group Representations and Quantization, p. 147, J. HENNIG, W. LÜCKE and J. TOLAR Eds., Lect. Notes Phys., Vol. 379, Springer-Verlag, Berlin, 1991. | MR