The Abel transform and shift operators
Beerends, R. J.
Compositio Mathematica, Tome 68 (1988), p. 145-197 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1988-01-01
@article{CM_1988__66_2_145_0,
     author = {Beerends, R. J.},
     title = {The Abel transform and shift operators},
     journal = {Compositio Mathematica},
     volume = {68},
     year = {1988},
     pages = {145-197},
     mrnumber = {945549},
     zbl = {0661.43006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1988__66_2_145_0}
}

Beerends, R. J. The Abel transform and shift operators. Compositio Mathematica, Tome 68 (1988) pp. 145-197. http://gdmltest.u-ga.fr/item/CM_1988__66_2_145_0/

1 K. Aomoto: Sur les transformations d'horisphère et les équations intégrales qui s'y rattachent, J. Fac. Sci. Univ. Tokyo 14 (1967) 1-23. | MR 222218 | Zbl 0177.41801

2 R.J. Beerends: On the Abel transform and its inversion. Thesis, University of Leiden (1987). | MR 935586

3 N. Bourbaki: Eléments de Mathématique, Groupes et algèbres de Lie, Chapitres 4, 5 et 6, Hermann, Paris (1968). | MR 453824 | Zbl 0483.22001

4 J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan: Spectra of compact locally symmetric manifolds of negative curvature, Invent. Math. 52 (1979) 27-93. | MR 532745 | Zbl 0434.58019

5 R. Gangolli: Asymptotic behaviour of spectra of compact quotients of certain symmetric spaces, Acta Math. 121 (1968) 151-192. | MR 239000 | Zbl 0169.46004

6 A. Hba: Sur l'inversion de la transformation d'Abel, preprint 92, Univ. de Nice (1986).

7 G.J. Heckman and E.M. Opdam: Root systems and hypergeometric functions I, Comp. Math. 64 (1987) 329-352. | Numdam | MR 918416 | Zbl 0656.17006

8 S. Helgason: Differential geometry, Lie groups, and symmetric spaces, Academic Press, New York (1978). | MR 514561 | Zbl 0451.53038

9 S. Helgason: Groups and geometric analysis, Academic Press, Orlando (1984). | MR 754767 | Zbl 0543.58001

10 T.H. Koornwinder: Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators I-IV, Indag. Math. 36 (1974) 48-66 and 358-381. | MR 340673 | Zbl 0263.33011 | Zbl 0267.33008

11 T.H. Koornwinder: A new proof of a Paley-Wiener type theorem for the Jacobi transform, Ark. Mat. 13 (1975) 145-159. | MR 374832 | Zbl 0303.42022

12 N. Lohoué and T. Rychener: Die Resolvente von Δ auf symmetrischen Räumen vom nichtkompakten Typ, Comment. Math. Helv. 57 (1982) 445-468. | Zbl 0505.53022

13 C. Meaney: The inverse Abel transform for SU(p, q), Ark. Mat. 24 (1968) 131-140. | MR 852831 | Zbl 0608.43008

14 E.M. Opdam: Root systems and hypergeometric functions III. To appear in Comp. Math. (1988). | Numdam | MR 949270 | Zbl 0669.33007

15 F. Rouvière: Sur la transformation d'Abel des groupes de Lie semisimples de rang un, Ann. Scuola Norm. Sup. Pisa 10 (1983) 263-290. | Numdam | MR 728437 | Zbl 0527.43006

16 J. Sekiguchi: Zonal spherical functions on some symmetric spaces, Publ. RIMS Kyoto Univ. 12 Suppl. (1977) 455-459. | MR 461040 | Zbl 0383.43005

17 I. Sprinkhuizen-Kuyper: Orthogonal polynomials in two variables; A further analysis of the polynomials orthogonal on a region bounded by two lines and a parabola, SIAM J. Math. Anal. 7 (1976) 501-518. | MR 415187 | Zbl 0332.33011

18 L. Vretare: Formulas for elementary spherical functions and generalized Jacobi polynomials, SIAM J. Math. Anal. 15 (1984) 805-833. | MR 747438 | Zbl 0549.43006

19 B.L. Van Der Waerden: Algebra I, 8. aufl., Springer, New York (1971).

20 A. Hba: Analyse harmonique sur (SL(3, H)), C.R. Acad. Sci. Paris Sér. I 305 (1987) 77-80. | MR 901139 | Zbl 0616.43011