A characterization of the higher dimensional groups associated with continuous wavelets

Journal of Geometric Analysis

Volumn 12, Issue 1, 2002, Pages 89-102

  Laugesen, R S ^a   Weaver, N ^b   Weiss, G L ^b   Wilson, E N ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b WASHINGTON UNIVERSITY   (United States)

Author keywords

admissable dialatin groups; continuous wavelets; discrete wavelets

Indexed keywords

EID: 84867922891     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02930862     Document Type: Article

References (20)

1. Ali, S. T.; Antoine, J.-P.; and Gazeau, J.-P.,Coherent States, Wavelets and Their Generalizations, Springer-Verlag, Inc.; New York, (2000).
2. Bacry, H.; Grossman, A.; and Zak, J.Geometry of Generalized Coherent States, Group Theoretical Methods in Physics (Fourth International Colloquium, Nijmegen, 1975), Springer-Verlag, Berlin, Lecture Notes in Physics,50, 249-268, (1978).
3. D. Bernier K.F. Taylor 1996 Wavelets from square-integrable representations SIAM J. Math. Anal. 27 2 594 608 0843.42018 10.1137/ S0036141093256265 1377491
4. rd Eur. Conf. in Mathematics, July, (2000).
5. A.P. Calderón 1964 Intermediate spaces and interpolation, the complex method Stud. Math. 24 113 190 0204.13703
6. A.L. Carey 1976 Square integrable representations of non-unimodular groups Bull. Austral. Math. Soc. 15 1 12 0327.22008 430146 10.1017/ S0004972700036728
7. Chui, C.; Czaja, W.; Maggioni, M.; and Weiss, G.L. Characterization of general tight wavelet frames with matrix dilation and tightness preserving oversampling, to appear inJ. Four. Anal. and Applications.
8. Corbett, J. Coherent States on Kinematic Groups: The Study of Spatio-Temporal Wavelets and Their Applications to Motion Estimation, Ph.D. Thesis, Washington University, (1999).
9. M. Duflo C.C. Moore 1976 On the representation of a nonunimodular locally compact group J. Funct. Anal. 21 209 243 0317.43013 10.1016/0022-1236(76)90079- 3 393335
10. DeMari, F. and Nowak, K. Reproducing formulas and commutative operator algebras related to affine transformations of the time-frequency plane, preprint.
11. H. Führ 1996 Wavelet frames and admissibility in higher dimensions J. of Math. Phys. 37 6353 6366 0864.44003 10.1063/1.531752
12. Führ, H. Continuous wavelet transforms from semidirect products, to appear inRevista Ciencias Matematicas.
13. Führ, H. Admissible vectors for the regular representations, to appear inProc. Am. Math. Soc.
14. Führ, H. and Mayer, M. Continuous wavelet transforms from cyclic representations: A general approach using plancherel measure, preprint, (1999).
15. C.E. Heil D.F. Walnut 1989 Continuous and discrete wavelet transforms SIAM Review 31 628 666 0683.42031 10.1137/1031129 1025485
16. C.J. Isham J.R. Klauder 1991 Coherent states forn-dimensional Euclidean groups and their application J. of Math. Phys. 32 607 620 0735.22012 10.1063/1.529402 1093798
17. Kalisa, C. Etats Cohérents Affines: Canoniques, Galiléns et Relativistes, Ph.D. Thesis, Université Louvaine, (1993).
18. H. Liu L. Peng 1997 Admissible wavelets associated with the Heisenberg group Pacific J. of Math. 180 101 123 1474896 10.2140/pjm.1997.180.101
19. Weiss, G.L. and Wilson, E.N.The Mathematical Theory of Wavelets, Proceedings of the NATO-ASI meeting, Harmonic Analysis 2000-A Celebration, Kluwer Publisher, to appear in 2001.
20. Zimmer, R.J.Ergodic Theory and Semisimple Groups, Birkhäuser, Boston, (1980).