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Favard’s Theorem Modulo an Ideal

  • Franciszek Hugon Szafraniec
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 157)

Abstract

Recently a treatise [2] dealing with the three term recurrence relation for polynomials orthogonal on algebraic sets was born. Because the paper is pretty sizeable in volume and rich in essence a kind of assistance in the matter as well as some invitation to it has become a need.

Keywords

Polynomials in several variables orthogonal polynomials three term recurrence relation Favard’s theorem ideal of polynomials algebraic set Zariski’s topology symmetric operator selfadjoint operator joint spectral measure product polynomials Krawchouk polynomials Charlier polynomials 

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References

  1. [1]
    T.S. Chihara, An introduction to orthogonal polynomials, in Mathematics and its Applications, vol. 13, Gordon and Breach, New York, 1978.Google Scholar
  2. [2]
    D. Cichoń, J. Stochel and F.H. Szafraniec, Three term recurrence relation modulo an ideal and orthogonality of polynomials of several variables, J. Approx. Theory, to appear.Google Scholar
  3. [3]
    R. Koekoek and R.F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Delft University of Technology, Report of the Faculty of Technical Mathematics and Informatics no. 94-05.Google Scholar
  4. [4]
    W. Schoutens, Stochastic processes and orthogonal polynomials, in Lecture Notes in Statistics, vol. 145, Springer-Verlag, New York — Berlin — Heidelberg, 2000.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Franciszek Hugon Szafraniec
    • 1
  1. 1.Instytut MatematykiUniwersytet JagiellońskiKrakówPoland

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