The Abel transform and shift operators

R. J. Beerends

Compositio Mathematica (1988)

  • Volume: 66, Issue: 2, page 145-197
  • ISSN: 0010-437X

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Beerends, R. J.. "The Abel transform and shift operators." Compositio Mathematica 66.2 (1988): 145-197. <http://eudml.org/doc/89902>.

@article{Beerends1988,
author = {Beerends, R. J.},
journal = {Compositio Mathematica},
keywords = {noncompact connected real semisimple Lie group; Lie algebra; Iwasawa decomposition; restricted roots; Weyl group; spaces of - functions with compact support; spherical Fourier transform; inversion of the Abel transform; differential operators; root systems; Laplace- Beltrami operator},
language = {eng},
number = {2},
pages = {145-197},
publisher = {Kluwer Academic Publishers},
title = {The Abel transform and shift operators},
url = {http://eudml.org/doc/89902},
volume = {66},
year = {1988},
}

TY - JOUR
AU - Beerends, R. J.
TI - The Abel transform and shift operators
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 66
IS - 2
SP - 145
EP - 197
LA - eng
KW - noncompact connected real semisimple Lie group; Lie algebra; Iwasawa decomposition; restricted roots; Weyl group; spaces of - functions with compact support; spherical Fourier transform; inversion of the Abel transform; differential operators; root systems; Laplace- Beltrami operator
UR - http://eudml.org/doc/89902
ER -

References

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  2. 2 R.J. Beerends: On the Abel transform and its inversion. Thesis, University of Leiden (1987). Zbl0597.43006MR935586
  3. 3 N. Bourbaki: Eléments de Mathématique, Groupes et algèbres de Lie, Chapitres 4, 5 et 6, Hermann, Paris (1968). Zbl0483.22001MR453824
  4. 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. Zbl0434.58019MR532745
  5. 5 R. Gangolli: Asymptotic behaviour of spectra of compact quotients of certain symmetric spaces, Acta Math.121 (1968) 151-192. Zbl0169.46004MR239000
  6. 6 A. Hba: Sur l'inversion de la transformation d'Abel, preprint 92, Univ. de Nice (1986). 
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  8. 8 S. Helgason: Differential geometry, Lie groups, and symmetric spaces, Academic Press, New York (1978). Zbl0451.53038MR514561
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  10. 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. MR340673
  11. 11 T.H. Koornwinder: A new proof of a Paley-Wiener type theorem for the Jacobi transform, Ark. Mat.13 (1975) 145-159. Zbl0303.42022MR374832
  12. 12 N. Lohoué and T. Rychener: Die Resolvente von Δ auf symmetrischen Räumen vom nichtkompakten Typ, Comment. Math. Helv.57 (1982) 445-468. Zbl0505.53022
  13. 13 C. Meaney: The inverse Abel transform for SU(p, q), Ark. Mat.24 (1968) 131-140. Zbl0608.43008MR852831
  14. 14 E.M. Opdam: Root systems and hypergeometric functions III. To appear in Comp. Math. (1988). Zbl0669.33007MR949270
  15. 15 F. Rouvière: Sur la transformation d'Abel des groupes de Lie semisimples de rang un, Ann. Scuola Norm. Sup. Pisa10 (1983) 263-290. Zbl0527.43006MR728437
  16. 16 J. Sekiguchi: Zonal spherical functions on some symmetric spaces, Publ. RIMS Kyoto Univ.12 Suppl. (1977) 455-459. Zbl0383.43005MR461040
  17. 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. Zbl0332.33011MR415187
  18. 18 L. Vretare: Formulas for elementary spherical functions and generalized Jacobi polynomials, SIAM J. Math. Anal.15 (1984) 805-833. Zbl0549.43006MR747438
  19. 19 B.L. van der Waerden:Algebra I, 8. aufl., Springer, New York (1971). 
  20. 20 A. Hba: Analyse harmonique sur (SL(3, H)), C.R. Acad. Sci. Paris Sér. I305 (1987) 77-80. Zbl0616.43011MR901139

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