Sur la transformation de Radon de la sphère S d

Ahmed Abouelaz; Radouan Daher

Bulletin de la Société Mathématique de France (1993)

  • Volume: 121, Issue: 3, page 353-382
  • ISSN: 0037-9484

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Abouelaz, Ahmed, and Daher, Radouan. "Sur la transformation de Radon de la sphère $S^d$." Bulletin de la Société Mathématique de France 121.3 (1993): 353-382. <http://eudml.org/doc/87670>.

@article{Abouelaz1993,
author = {Abouelaz, Ahmed, Daher, Radouan},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Radon transform on the sphere; inversion formula; Plancherel formula; dual Radon transform; Laplace-Beltrami-Operator},
language = {fre},
number = {3},
pages = {353-382},
publisher = {Société mathématique de France},
title = {Sur la transformation de Radon de la sphère $S^d$},
url = {http://eudml.org/doc/87670},
volume = {121},
year = {1993},
}

TY - JOUR
AU - Abouelaz, Ahmed
AU - Daher, Radouan
TI - Sur la transformation de Radon de la sphère $S^d$
JO - Bulletin de la Société Mathématique de France
PY - 1993
PB - Société mathématique de France
VL - 121
IS - 3
SP - 353
EP - 382
LA - fre
KW - Radon transform on the sphere; inversion formula; Plancherel formula; dual Radon transform; Laplace-Beltrami-Operator
UR - http://eudml.org/doc/87670
ER -

References

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  1. [1] BEERENDS (R.). — On the Abel Transform and its Inversion, Ph. D. Thesis, Leiden University, 1987. 
  2. [2] ERDELYI (A.), MAGNUS (W.), OBERHETTINGER (F.) and TRICOMI (F.G.). — Tables of Integral Transforms, vol. 3. — Mc Graw-Hill, New-York, 1954. 
  3. [3] FARAUT (J.). — Analyse harmonique et fonctions spéciales, École d'été d'analyse harmonique de Tunis, 1984. 
  4. [4] FARAUT (J.). — Analyse harmonique. — C.I.M.P.A, 1982. 
  5. [5] GUELFAND (I.M.), GRAEV (I.M.) and VILENKIN (N.J.). — Géométrie intégrale et théorie des représentations. — Monographies Universitaires de Mathématiques, vol. 5, Dunod, 1962. 
  6. [6] GUELFAND (I.M.) and CHILOV (G.E.). — Les distributions. — Collection Universitaire de Mathématiques, Dunod, 1962. Zbl0115.10102MR24 #A2235
  7. [7] HELGASON (S.). — Groups and geometric analysis. — Academic Press, 1984. Zbl0543.58001MR86c:22017
  8. [8] HELGASON (S.). — A duality for symmetric spaces with applications to group representations, Advan. Math., t. 5, 1970, p. 1-154. Zbl0209.25403MR41 #8587
  9. [9] HELGASON (S.). — The Radon transform on Euclidean spaces, Compact two-point Homogeneous Spaces and Grassmann Manifolds, Acta. Math., t. 113, 1965, p. 153-180. Zbl0163.16602MR30 #2530
  10. [10] KOORNWINDER (T.H.). — A New Proof a Paley-Wiener Theorem for the Jacobi-transform, Arkiv for Math., t. 13, 1975. Zbl0303.42022MR51 #11028
  11. [11] KOORNWINDER (T.H.). — Jacobi Functions and Analysis on Non Compact Semi-simple Lie Groups, in Special Functions. — R.A. Askey et al., Reidel Pub. Comp., 1984, p. 1-85. Zbl0584.43010MR86m:33018
  12. [12] SHERMAN (T.). — Fourier Analysis on the Sphere, Trans. Amer. Math. Soc., t. 209, 1975, p. 1-31. Zbl0308.43009MR52 #11486
  13. [13] STRICHARTZ (R.S.). — LP-Estimates for Radon Transforms in Euclidean and non Euclidean Spaces, Duke Math. J., t. 48, 1981, p. 699-727. Zbl0477.44003MR86k:43008
  14. [14] TITCHMARSH (E.C.). — The Theory of Functions, 2nd ed. — Oxford Univ. Press, London and New-York, 1939. JFM65.0302.01
  15. [15] TRIMECHE (K.). — Transformation intégrale de Weyl et théorème de Paley-Wiener associés à un opérateur différentiel singulier sur (0, ∞), J. Math. Pures et Appl., t. 60, 1981, p. 51-98. Zbl0416.44002MR83i:47058

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