Coherent states of the 1+1 dimensional Poincaré group : square integrability and a relativistic Weyl transform
Annales de l'I.H.P. Physique théorique, Tome 51 (1989) no. 1, pp. 23-44. 
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     author = {Ali, S. Twareque and Antoine, J.-P.},
     title = {Coherent states of the 1+1 dimensional {Poincar\'e} group : square integrability and a relativistic {Weyl} transform},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {23--44},
     publisher = {Gauthier-Villars},
     volume = {51},
     number = {1},
     year = {1989},
     mrnumber = {1029848},
     zbl = {0702.22024},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1989__51_1_23_0/}
}
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Ali, S. Twareque; Antoine, J.-P. Coherent states of the 1+1 dimensional Poincaré group : square integrability and a relativistic Weyl transform. Annales de l'I.H.P. Physique théorique, Tome 51 (1989) no. 1, pp. 23-44. http://www.numdam.org/item/AIHPA_1989__51_1_23_0/

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

[2] A. Perelomov, Generalized Coherent States and Their Applications, Springer, Berlin, 1986. | MR | Zbl

[3] J. Dixmier, Les C*-algèbres et leurs représentations, 2e éd., Gauthier-Villars, Paris, 1969. | MR | Zbl

[4] S.A. Gaal, Linear Analysis and Representation Theory, Springer, Berlin, 1973. | MR | Zbl

[5] M. Duflo and C.C. Moore, J. Funct. Anal., Vol. 21, 1976, p. 209. | Zbl

[6] A. Carey, Bull. Austral. Math. Soc., 15, 1976, p. 1; Rep. Math. Phys., Vol. 14, 1978, p. 247. | MR | Zbl

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

[8] M. Flensted-Jensen, Ann. of Math., Vol. 111, 1980, p. 253. | MR | Zbl

[9] H. Schlichtkrull, Invent. Math., Vol. 68, 1982, p. 497. | MR | Zbl

[10] S.T. Ali, Rivista del Nuovo Cim., Vol. 8, # 11, 1985, p. 1. | MR

[11] E. Prugovecki, Stochastic Quantum Mechanics and Quantum Spacetime, D. Reidel, Dordrecht, 1984. | MR | Zbl

[12] S.T. Ali and H.D. Doebner, Quantization, topology and ordering, in Lect. Notes in Physics, Vol. 278, Springer, Berlin, 1987. | MR

[13] A. Grossmann, G. Loupias and E.M. Stein, Ann. Inst. Fourier, Grenoble, Vol. 18, 1968, p. 343. | Numdam | MR | Zbl

[14] I. Daubechies and A. Grossmann, J. Math. Phys., Vol. 21, 1980, p. 2080. | MR

[15] I. Daubechies, A. Grossmann and J. Reignier, J. Math. Phys., Vol. 24, 1983, p. 239. | MR

[16] J.C.T. Pool, J. Math. Phys., Vol. 7, 1966, p. 66. | Zbl

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

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

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

[20] R. Kunze, Pacific J. Math., Vol. 53, 1974, p. 465. | MR | Zbl

[21] A. Borel, Représentations des Groupes Localement Compacts; Lect. Notes in Mathematics, Vol. 276, Springer, Berlin, 1972. | Zbl

[22] H. Moscovici, Commun. Math. Phys., Vol. 54, 1977, p. 63. | MR | Zbl

[23] A.A. Kirillov, Elements of the Theory of Representations, Springer, Berlin, 1976. | MR | Zbl

[24] H. Moscovici and A. Verona, Ann. Inst. H. Poincaré, Vol. 29, 1978, p. 139. | Numdam | MR | Zbl

[25] H. Scutaru, Lett. Math. Phys., 2, 1977, p. 101. | MR | Zbl

[26] A.M. Perelomov, Commun. Math. Phys., Vol. 26, 1972, p. 222 (reprinted in Ref. 1); ibid., Vol. 44, 1975, p. 197. | MR | Zbl

[27] I.M. Gel'Fand and N. Ya. Vilenkin, Generalized Functions, Vol. 4, Academic Press, New York, 1964.

[28] J.-P. Antoine, J. Math. Phys., Vol. 10, 1969, pp. 53, 2276. | Zbl

[29] E. Nelson, Annals of Math., Vol. 70, 1959, p. 570. | MR

[30] P. Bona, Czech. J. Phys., Vol. B33, 1983, p. 837.

[31] S.T. Ali and S. De Bièvre, in XYIth International Colloquium on Group-Theoretical Methods in Physics (Proceedings, Varna, 1987); Lecture Notes in Physics, Vol. 313, p. 201; H.-D. DOEBNER, J.-D. HENNIG, T. D. PALEV Eds., Springer, Berlin, 1988. | Zbl

[32] S. De Bièvre, J. Math. Phys., vol. 30, 1989, p. 1401. Toronto, 1988 (preprint). | MR | Zbl