Wavelet transform and orthogonal decomposition of L2 space on the cartan domain BDI(q = 2)

Transactions of the American Mathematical Society

Volumn 349, Issue 5, 1997, Pages 2049-2068

  Jiang, Qingtang ^a,b  

^a PEKING UNIVERSITY   (China)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Group; Orthogonal decomposition; Square integrable representation; Wavelet transform; Weyl poincar

Indexed keywords

EID: 21644490412     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-97-01727-3     Document Type: Article

References (16)

1. G. Bohnké, Treillis d'ondelettes associés aux groupes de Lorentz, Ann. Inst. Henri Poincaré Phys. Théor. 54 (1991), 245-259. MR 93c:22020
2. M. Duflo and C. Moore, On the regular representation of a nonunimodular locally compac group, J. Funct. Anal. 21 (1976), 209-243. MR 52:14145
3. J. Faraut and A. Korânyi, Analysis on symmetric cones, Clarendon Press, Oxford, 1994.
4. H. Feichtinger and K. Gröchenig, Banach spaces related to integrable group representation and their atomic decomposition. I, J. Funct. Anal. 86 (1989), 307-340. MR 91g:43011
5. A. Grossmann and J. Morlet, Decomposition of Hardy functions into square integrabl wavelets of constant shape, SIAM J. Math. Anal. 15 (1984), 723-736. MR 85i:81146
6. L. Hua, Harmonic analysis of several complex variables in classical domains, Amer. Math Soc., Providence, RI, 1963. MR 30 2162
7. Q. Jiang, Wavelet transform associated to the Weyl-Poincare group, preprint.
8. Q. Jiang and L. Peng, Phase space, wavelet transform and Toeplitz-Hankel type operators Israel J. Math. 89 (1995), 157-171. MR 96a:47047
9. A. Perelomov, Generalized coherent states and their applications, Springer-Verlag, Berlin 1986. MR 87m 22035
10. E. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeto University Press, Princeton, NJ, 1971. MR 46 4102
11. G. Szegö, Orthogonal polynomials, 3rd éd., Amer. Math. Soc. Colloq. Pub., Vol. 23, 1967 MR 46:8631
12. M. Taylor, Noncommutative harmonie analysis, Amer. Math. Soc., Providence, RI, 1986 MR 88a 22021
13. A. Unterberger and J. Unterberger, A quantization of the Cartan domain BDI (q=2) an operators on the light cone, J. Funct. Anal. 72 (1987), 279-319. MR 88k:58152
14. A. Unterberger, Analyse harmonique et analyse pseudo-différentielle du cône de lumière Astérisque, no. 156, Soc. Math. France, 1987. MR 90d:58152
15. S. Vagi, Harmonie analysis on Cartan and Siegel domains, Studies in Harmonic Analysis, J A. Ash, eds., MAA, 1976, pp. 257-309. MR 57 16719
16. N. Vilenkin, Special functions and the theory of group representations, Amer. Math. Soc., Providence, RI, 1968. MR 37 5429