Determinantal formulas for zonal spherical functions on hyperboloids

Mathematische Annalen

Volumn 319, Issue 2, 2001, Pages 215-234

  Van Diejen, J F ^a   Kirillov, A N ^b  

^a UNIVERSITY OF CHILE   (Chile)

^b NAGOYA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035583474     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004433     Document Type: Article

References (19)

1. G.E. Andrews, R. Askey, and R. Roy, Special Functions, Cambridge University Press, Cambridge, 1999.
2. A.O. Barut, A. Inomata, and R. Wilson, A new realisation of dynamical groups and factorisation method. J. Phys. A.: Math. Gen. 20 (1987), 4075-4082.
3. A.O. Barut, A. Inomata, and R. Wilson, Algebraic treatment of second Pöschl-Teller, Morse-Rosen and Eckart equations. J. Phys. A.: Math. Gen. 20 (1987), 4083-4096.
4. A.O. Barut and R. Raczka, Theory of Group Representations and Applications, (second revised edition). World Scientific, Singapore, 1986.
5. J.F. van Diejen and A.N. Kirillov, A combinatorial formula for the associated Legendre functions of integer degree. Adv. Math. 149 (2000), 61-88.
6. J.F. van Diejen and H. Puschmann, Reflectionless Schrödinger operators, the dynamics of zeros, and the solitonic Sato formula, Duke Math. J. 104 (2000), 269-318.
7. P. Deift and E. Trubowitz, Inverse scattering on the line. Comm. Pure and Appl. Math. 32 (1979), 121-251.
8. N.M. Ercolani, C.D. Levermore, and T. Zhang, The behavior of the Weyl function in the zero-dispersion KdV limit. Commun. Math. Phys. 183 (1997), 119-143.
9. A. Erdélyi et al, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York, 1953.
10. S. Flügge, Practical Quantum Mechanics 1. Springer-Verlag, Berlin, 1971.
11. G.J. Heckman and H. Schlichtkrull, Harmonic Analysis and Special Functions on Symmetric Spaces. Perspectives in Math. 16, Academic Press, San Diego, 1994.
12. S. Helgason, Groups and Geometric Analysis. Academic Press, Orlando, 1984.
13. S. Helgason, Geometric Analysis on Symmetric Spaces. Amer. Math. Soc., Providence, R.I., 1994.
14. T.H. Koornwinder, Jacobi functions and analysis on noncompact semisimple Lie groups. In: R.A. Askey, T.H. Koornwinder, and W. Schempp (eds.), Special Functions: Group Theoretical Aspects and Applications. D. Reidel Publishing Company, Dordrecht, 1984, pp. 1-85.
15. I.G. Macdonald, Symmetric Functions and Hall Polynomials, (second edition). Oxford University Press, Oxford, 1995.
16. S. Novikov, S.V. Manakov, L.P. Pitaevskii, and V.E. Zakharov, Theory of Solitons: The Inverse Scattering Method. Consultants Bureau, New York, 1984.
17. M.A. Olshanetsky and A.M. Perelomov, Quantum integrable systems related to Lie algebras. Phys. Rep. 94 (1983), 313-404.
18. J. Sekiguchi, Eigenspaces of the Laplace-Beltrami operator on a hyperboloid. Nagoya Math. J. 79 (1980), 151-185.
19. E.C. Titchmarsh, Eigenfunction Expansions Associated with Second-order Differential Equations, Part 1, (second edition). Oxford University Press, Oxford, 1962.