Root systems and hypergeometric functions IV

E. M. Opdam

Compositio Mathematica (1988)

  • Volume: 67, Issue: 2, page 191-209
  • ISSN: 0010-437X

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Opdam, E. M.. "Root systems and hypergeometric functions IV." Compositio Mathematica 67.2 (1988): 191-209. <http://eudml.org/doc/89916>.

@article{Opdam1988,
author = {Opdam, E. M.},
journal = {Compositio Mathematica},
keywords = {multivariable hypergeometric functions; complete integrability; Hamiltonian systems; root systems},
language = {eng},
number = {2},
pages = {191-209},
publisher = {Kluwer Academic Publishers},
title = {Root systems and hypergeometric functions IV},
url = {http://eudml.org/doc/89916},
volume = {67},
year = {1988},
}

TY - JOUR
AU - Opdam, E. M.
TI - Root systems and hypergeometric functions IV
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 67
IS - 2
SP - 191
EP - 209
LA - eng
KW - multivariable hypergeometric functions; complete integrability; Hamiltonian systems; root systems
UR - http://eudml.org/doc/89916
ER -

References

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  1. [C] F. Calogero: Solution of the one dimensional N-body problems with quadratic and/or inversely quadratic pair potentials, J. Math. Physics12 (1971) 419-436. Zbl1002.70558MR280103
  2. [H] G.J. Heckman: Root systems and hypergeometric functions II, Comp. Math.64 (1987) 353-373. Zbl0656.17007MR918417
  3. [Ha] Harish-Chandra: Spherical functions on a semisimple Lie group I, Amer. J. Math.80 (1958) 241-310. Zbl0093.12801MR94407
  4. [Hel] S. Helgason: Groups and Geometric Analysis. Academic Press (1984). Zbl0543.58001MR754767
  5. [Hö] L. Hörmander: An Introduction to Complex Analysis in Several Variables, van Nostrand (1966). Zbl0138.06203MR203075
  6. [HO] G.J. Heckman and E.M. Opdam: Root systems and hypergeometric functions I, Comp. Math.64 (1987) 329-352. Zbl0656.17006MR918416
  7. [J] C. Jacobi: Problema trium corporum mutis attractionibus cubus distantiarum inverse proportionalibus recta linea se moventium, Gesammelte Werke 4, Berlin (1866). 
  8. [K] T.H. Koornwinder: Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent differential operators, I-IV, Indag. Math.36 (1974) 48-66 and 358-381. MR340673
  9. [Mac] I.G. Macdonald: unpublished manuscript (1985). 
  10. [Mar] C. Marchioro: Solution of a three body scattering problem in one dimension, J. Math. Physics11 (1970) 2193-2196. 
  11. [Mo] J. Moser: Three integrable Hamiltonian systems connected with isospectral deformation, Adv. Math.16197-220 (1975). Zbl0303.34019MR375869
  12. [Op] E.M. Opdam: Root systems and hypergeometric functions III, Comp. Math.67 (1988) 21-50. Zbl0669.33007MR949270
  13. [OP] M.A. Olshanetsky and A.M. Perelemov: Completely integrable Hamiltonian systems connected with semisimple Lie algebras, Inv. Math.37 (1976) 93-108. Zbl0342.58017MR426053
  14. [Se] J. Sekiguchi: Zonal spherical functions on some symmetric spaces, Publ. R.M.S. Kyoto. Univ. 12 Suppl. (1977) 455-459. Zbl0383.43005MR461040

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