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Computational Methods and Function Theory

, Volume 2, Issue 2, pp 519–537 | Cite as

Discrete Spectra of Certain Co-Recursive Pollaczek Polynomials and its Applications

  • Alexandre I. Aptekarev
  • André Draux
  • Dmitrii Toulyakov
Article

Abstract

For a special class of co-recursive Pollaczek polynomials the discrete part of the measure of orthogonality is determined. The results are applied for the determination of the fundamental frequencies of a certain class of Stieltjes-Krein discrete strings. Connections with best constants in Markov-Bernstein inequalities with integral norms are considered, too.

Keywords

Orthogonal polynomials Laguerre polynomials Meixner polynomials Pollaczek polynomials Markov-Bernstein inequalities zeros of polynomials discrete spectrum discrete string 

2000 MSC

33C45 

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Copyright information

© Heldermann  Verlag 2002

Authors and Affiliations

  • Alexandre I. Aptekarev
    • 1
  • André Draux
    • 2
  • Dmitrii Toulyakov
    • 3
  1. 1.Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia
  2. 2.Département de Génie MathématiqueINSA de RouenMont-Saint-Aignan CedexFrance
  3. 3.Department of Applied MathematicsNizhnii Novgorod Technical UniversityN-NovgorodRussia

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