Wavelet transform associated to an induced representation of S L ( n + 2 , R )

Takeshi Kawazoe

Annales de l'I.H.P. Physique théorique (1996)

  • Volume: 65, Issue: 1, page 1-13
  • ISSN: 0246-0211

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Kawazoe, Takeshi. "Wavelet transform associated to an induced representation of $SL (n + 2, R)$." Annales de l'I.H.P. Physique théorique 65.1 (1996): 1-13. <http://eudml.org/doc/76735>.

@article{Kawazoe1996,
author = {Kawazoe, Takeshi},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {locally compact group; Hilbert space; character; induced representation; Heisenberg group; wavelet transforms; semisimple Lie groups},
language = {eng},
number = {1},
pages = {1-13},
publisher = {Gauthier-Villars},
title = {Wavelet transform associated to an induced representation of $SL (n + 2, R)$},
url = {http://eudml.org/doc/76735},
volume = {65},
year = {1996},
}

TY - JOUR
AU - Kawazoe, Takeshi
TI - Wavelet transform associated to an induced representation of $SL (n + 2, R)$
JO - Annales de l'I.H.P. Physique théorique
PY - 1996
PB - Gauthier-Villars
VL - 65
IS - 1
SP - 1
EP - 13
LA - eng
KW - locally compact group; Hilbert space; character; induced representation; Heisenberg group; wavelet transforms; semisimple Lie groups
UR - http://eudml.org/doc/76735
ER -

References

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  1. [AAG1] S.T. Ali, J.-P. Antoine and J.-P. Gazeau, Square integrability of group representations on homogenous space. I. Reproducing triples and frames, Ann. Inst. H. Poincaré, Vol. 55, 1991, pp. 829-855. Zbl0752.22002MR1144104
  2. [AAG2] 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 Poincaré group, Ann. Inst. H. Poincaré, Vol. 55, 1991, pp. 857-890. Zbl0752.22003MR1144105
  3. [B] G. Bohnke, Treillis d'ondelettes associés aux groupes de Lorentz, Ann. Inst. H. Poincaré, Vol. 54, 1991, pp. 245-259. Zbl0743.43005MR1122655
  4. [DM] M. Duflo and C.C. Moore, On the regular representation of a nonunimodular locally compact group, J. Funct. Anal., Vol. 21, 1976, pp. 209-243. Zbl0317.43013MR393335
  5. [F] G.B. Folland, Harmonic Analysis in Phase Space, Annals of Mathematics Studies, Vol. 122, Princeton University Press, Princeton, New Jersey, 1989. Zbl0682.43001MR983366
  6. [G] D. Geller, Spherical harmonics, the Weyl transform and the Fourier transform on the Heisenberg group, Canad. J. Math., Vol. 36, 1984, pp. 615-684. Zbl0596.46034MR756538
  7. [H1] Harish-Chandra, Harmonic analysis on real reductive groups I, J. Funct. Anal., Vol. 19, 1975, pp. 104-204. Zbl0315.43002MR399356
  8. [H2] Harish-Chandra, Harmonic analysis on real reductive groups II, Inv. Math., Vol. 36, 1976, pp. 1-55. Zbl0341.43010MR439993
  9. [H3] Harish-Chandra, Harmonic analysis on real reductive groups III, Ann. of Math., Vol. 104, 1976, pp. 127-201. Zbl0331.22007
  10. [HW] C.E. Heil and D.F. Walnut, Continuous and discrete wavelet transforms, SIAM Review, Vol. 31, 1989, pp. 628-666. Zbl0683.42031MR1025485
  11. [K] T. Kawazoe, A transform on classical bounded symmetric domains associated with a holomorphic discrete series, Tokyo J. Math., Vol. 12, 1989, pp. 269-297. Zbl0702.22013MR1030496
  12. [KT] C. Kalisa and B. Torrésani, N-dimensional affine Weyl-Heisenberg wavelets, Ann. Inst. H. Poincaré, Vol. 59, 1993, pp. 201-236. Zbl0923.43004MR1277217
  13. [Sa] P.J. Sally, Analytic Continuation of the Irreducible Unitary Representations of the Universal Covering Group of SL (2, R), Memoirs of A.S.M., 69, American Mathematical Society, Providence, Rhode Island, 1967. Zbl0157.20702MR235068
  14. [Su] M. Sugiura, Unitary Representations and Harmonic Analysis, An Introduction, Second Edition, North-Holland/Kodansha, Amsterdam/Tokyo, 1990. Zbl0697.22001MR1049151
  15. [T1] B. Torrésani, Wavelets associated with representations of the affine Weyl-Heisenberg group, J. Math. Phys., Vol. 32, 1991, pp. 1273-1279. Zbl0748.46046MR1103481
  16. [T2] B. Torrésani, Time-frequency representation: wavelet packets and optimal decomposition, Ann. Inst. H. Poincaré, Vol. 56, 1992, pp. 215-234. Zbl0760.42021MR1155278
  17. [VP] Van Dijk and M. Poel, The Plancherel formula for the pseudo-Riemannian space SL(n, R)/GL(n - 1, R), Comp. Math., Vol. 58, 1986, pp. 371-397. Zbl0593.43009MR846911
  18. [Wal] N.R. Wallach, Harmonic Analysis on Homogeneous Spaces, Marcel Dekker, New York, 1973. Zbl0265.22022MR498996
  19. [War] G. Warner, Harmonic Analysis on Semi-Simple Lie Groups II, Springer-Verlag, Berlin, 1972. Zbl0265.22021MR499000

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