@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://www.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://www.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://www.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://www.numdam.org/item/AIHPA_1991__55_4_829_0/
[1] Ann. Inst. H. Poincaré, Phys. Théor., Vol. 51, 1989, p. 23. | Numdam | MR | Zbl
and ,[2] Ann. Inst. H. Poincaré, Phys. Théor., Vol. 52, 1990, p. 83. | Numdam | MR | Zbl
, and ,[3] Generalized Coherent States and their Applications, Springer-Verlag, Berlin, 1986. | MR | Zbl
,[4] Coherent States-Applications in Physics and Mathematical Physics, World Scientific, Singapore, 1985. | MR | Zbl
and ,[5] Rivista Nuovo Cim, Vol. 8, #11, 1985, pp. 1-128. | MR
,[6] Acta Appl. Math., Vol. 6, 1986, p. 1. | MR | Zbl
and ,[7] Acta Appl. Math., Vol. 6, 1986, p. 19. | MR | Zbl
and ,[8] Acta Appl. Math., Vol. 6, 1986, p. 47. | MR | Zbl
and ,[9] S.I.A.M. J. Math. Anal., Vol. 15, 1984, p. 723. | MR | Zbl
and ,[10] Trans. Am. Math. Soc., Vol. 72, 1952, p. 341. | MR | Zbl
and ,[11] J. Math. Phys., Vol. 27, 1986, p. 1271. | MR | Zbl
, and ,[12] I.E.E.E. Trans. Inform. Theory, Vol. 36, 1990, p. 961. | MR | Zbl
,[13] 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] S.I.A.M. Review, Vol. 31, 1989, p. 628. | MR | Zbl
and ,[16] 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
, and ,[17] Notes on Spectral Theory, Van Nostrand, Princeton, N.J., 1966. | MR | Zbl
,[18] Theory of Operator Algebras I, Springer-Verlag, Berlin, 1979, Chap. IV, Sec. 8. | Zbl
,[19] Les algèbres d'opérateurs dans l'espace hilbertien (Algèbres de von Neumann), Gauthier-Villars, Paris, 1957, 1969. | Zbl
,[20] Am. Math. Soc. Trans. Ser. 2, Vol. 5, 1975, p. 35.
,[21] Hilbertsche Räume mit Kernfunction, Springer-Verlag, Berlin, 1962. | Zbl
,[22] Continuous Frames in Hilbert Space (in preparation). | Zbl
, and ,[23] J. Math. Phys., Vol. 26, 1985, p. 2473; Ann. Inst. H. Poincaré, Phys. Théor., Vol. 45, 1986, p. 293. | Numdam | MR | Zbl
, and ,[24] Invent. Math., Vol. 105, 1991, p. 157. , Inverse Radon Transforms Through Inverse Wavelet Transforms, Inverse Problems (to appear). | MR | Zbl
and ,[25] J. Math. Phys., Vol. 30, 1989, p. 1401. | Zbl
,[26] 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
and ,