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

How to cite

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.