Skip to main content
SpringerLink
Log in

Special orthogonal polynomial systems mapped onto each other by the Fourier-Jacobi transform

  • II. Conferenciers Ou Contributeurs
  • Conference paper
  • First Online:
Book cover Polynômes Orthogonaux et Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1171))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C.P. Boyer & F. Ardalan, On the decomposition SO(p,1)⊃SO(p−1,1) for most degenerate representations, J. Math. Phys. 12(1971), 2070–2075.

    Article  MathSciNet  MATH  Google Scholar 

  2. J.T. Broad, Extraction of continuum properties from L 2 basis set matrix representations of the Schrödinger equation: The Sturm sequence polynomials and Gauss quadrature, in “Numerical integration of differential equations and large linear systems” (J. Hinze, ed.), Lecture Notes in Math. 968, Springer, 1982, pp. 53–70.

    Google Scholar 

  3. D.J. Diestler, The discretization of continuous infinite sets of coupled ordinary linear differential equations: Application to the collision-induced dissociation of a diatomic molecule by an atom, ibidem, pp. 40–52.

    Google Scholar 

  4. N. Dunford & J.T. Schwartz, Linear operators II, Interscience, 1963.

    Google Scholar 

  5. C.F. Dunkl, Orthogonal polynomials with symmetry of order three, preprint, 1983.

    Google Scholar 

  6. A. Erdélyi e.a., Higher transcendental functions I, II, McGraw-Hill, 1953.

    Google Scholar 

  7. A. Erdélyi e.a., Tables of integral transforms II, McGraw-Hill, 1954.

    Google Scholar 

  8. J. Faraut, Un théorème de Paley-Wiener pour la transformation de Fourier sur un espace Riemannien symétrique de rang un, J. Funct. Anal. 49 (1982), 230–268.

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Flensted-Jensen, Spherical functions on a simply connected semisimple Lie group II. The Paley-Wiener theorem for the rank one case, Math. Ann. 228 (1977), 65–92.

    Article  MathSciNet  MATH  Google Scholar 

  10. T.H. Koornwinder, A new proof of a Paley-Wiener type theorem for the Jacobi transform, Ark. Mat. 13 (1975), 145–159.

    Article  MathSciNet  MATH  Google Scholar 

  11. T.H. Koornwinder, Jacobi functions and analysis on noncompact semisimple Lie groups, in “Special functions: group theoretical aspects and applications” (R.A. Askey, T.H. Koornwinder & W. Schempp, eds.), Reidel, 1984, pp. 1–85.

    Google Scholar 

  12. J. Labelle, Tableau d' Askey: Polynômes orthogonaux hypergéométriques, Département de Mathématiques et d' Informatique, Université du Québec, Montréal.

    Google Scholar 

  13. B. Roehner & G. Valent, Solving the birth and death processes with quadratic asymptotically symmetric transition rates, SIAM J. Appl. Math. 42 (1982), 1020–1046.

    Article  MathSciNet  MATH  Google Scholar 

  14. E.C. Titchmarsh, Eigenfunction expansions associated with second-order differential equations I, Oxford University Press, 2nd ed., 1962.

    Google Scholar 

  15. J.A. Wilson, Hypergeometric series, recurrence relations and some new orthogonal functions, Thesis, Univ. of Wisconsin, Madison, 1978.

    Google Scholar 

  16. J.A. Wilson, Some hypergeometric orthogonal polynomials, SIAM J. Math. Anal. 11 (1980), 690–701.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB, Amsterdam, The Netherlands

    T. H. Koornwinder

Authors
  1. T. H. Koornwinder
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Claude Brezinski André Draux Alphonse P. Magnus Pascal Maroni André Ronveaux

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Koornwinder, T.H. (1985). Special orthogonal polynomial systems mapped onto each other by the Fourier-Jacobi transform. In: Brezinski, C., Draux, A., Magnus, A.P., Maroni, P., Ronveaux, A. (eds) Polynômes Orthogonaux et Applications. Lecture Notes in Mathematics, vol 1171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076542

Download citation

  • DOI: https://doi.org/10.1007/BFb0076542

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16059-5

  • Online ISBN: 978-3-540-39743-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation