Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames
Ali, S. T. ; Antoine, J.-P. ; Gazeau, J.-P.
Annales de l'I.H.P. Physique théorique, Tome 54 (1991), p. 829-855 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPA_1991__55_4_829_0,
     author = {Ali, S. Twareque and Antoine, J.-P. and Gazeau, Jean-Pierre},
     title = {Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {54},
     year = {1991},
     pages = {829-855},
     mrnumber = {1144104},
     zbl = {0752.22002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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 54 (1991) pp. 829-855. http://gdmltest.u-ga.fr/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 1029848 | Zbl 0702.22024

[2] S.T. Ali, J.-P. Antoine and J.-P. Gazeau, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 52, 1990, p. 83. | Numdam | MR 1046086 | Zbl 0706.22018

[3] A. Perelomov, Generalized Coherent States and their Applications, Springer-Verlag, Berlin, 1986. | MR 899736 | Zbl 0605.22013

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

[5] S.T. Ali, Rivista Nuovo Cim, Vol. 8, #11, 1985, pp. 1-128. | MR 821194

[6] S.T. Ali and E. Prugovecki, Acta Appl. Math., Vol. 6, 1986, p. 1. | MR 837718 | Zbl 0603.22010

[7] S.T. Ali and E. Prugovecki, Acta Appl. Math., Vol. 6, 1986, p. 19. | MR 837719 | Zbl 0603.22011

[8] S.T. Ali and E. Prugovecki, Acta Appl. Math., Vol. 6, 1986, p. 47. | MR 837720 | Zbl 0603.22012

[9] A. Grossmann and J. Morlet, S.I.A.M. J. Math. Anal., Vol. 15, 1984, p. 723. | MR 747432 | Zbl 0578.42007

[10] R.J. Duffin and A.C. Schaeffer, Trans. Am. Math. Soc., Vol. 72, 1952, p. 341. | MR 47179 | Zbl 0049.32401

[11] I. Daubechies, A. Grossmann and Y. Meyer, J. Math. Phys., Vol. 27, 1986, p. 1271. | MR 836025 | Zbl 0608.46014

[12] I. Daubechies, I.E.E.E. Trans. Inform. Theory, Vol. 36, 1990, p. 961. | MR 1066587 | Zbl 0738.94004

[13] Y. Meyer, Ondelettes et Opérateurs I, II, Hermann, Paris, 1990. | MR 1085487 | Zbl 0694.41037

[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 1010895 | Zbl 0718.00009

[15] C.E. Heil and D.F. Walnut, S.I.A.M. Review, Vol. 31, 1989, p. 628. | MR 1025485 | Zbl 0683.42031

[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 1144105 | Zbl 0752.22003

[17] S.K. Berberian, Notes on Spectral Theory, Van Nostrand, Princeton, N.J., 1966. | MR 190760 | Zbl 0138.39104

[18] M. Takesaki, Theory of Operator Algebras I, Springer-Verlag, Berlin, 1979, Chap. IV, Sec. 8. | Zbl 0436.46043

[19] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien (Algèbres de von Neumann), Gauthier-Villars, Paris, 1957, 1969. | Zbl 0088.32304

[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 0103.08802

[22] S.T. Ali, J.-P. Antoine and J.-P. Gazeau, Continuous Frames in Hilbert Space (in preparation). | Zbl 0782.47019

[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 868528 | Zbl 0571.22021

[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 1109624 | Zbl 0751.35049

[25] S. De Bièvre, J. Math. Phys., Vol. 30, 1989, p. 1401. | Zbl 0686.46049

[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 1180088