Computational Methods and Function Theory 2 (2002), No. 2, 519--537
Copyright Heldermann Verlag 2002
Alexandre I. Aptekarev
aptekaa@spp.keldysh.ru, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Square 4, Moscow 125047, Russia.
André Draux
andre.draux@insa-rouen.fr, INSA de Rouen, Département de Génie Mathématique, Place Emile Blondel, BP 08, F-76131 Mont-Saint-Aignan Cedex, France.
Dmitrii Toulyakov
kalia@mail.nnov.ru, Nizhnii Novgorod Technical University, Department of Applied Mathematics, Minina Str. 24, N-Novgorod 603600, Russia.
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.
MSC 2000: 33C45.
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