Orthogonal Polynomials and their Applications -

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Résumé :
The Segovia meeting set out to stimulate an intensive exchange of ideas between experts in the area of orthogonal polynomials and its applications, to present recent research results and to reinforce the scientific and human relations among the increasingly international community working in orthogonal polynomials. This volume contains original research papers as well as survey papers about fundamental questions in the field (Nevai, Rakhmanov & L?pez) and its relationship with other fields such as group theory (Koornwinder), Pad? approximation (Brezinski), differential equations (Krall, Littlejohn) and numerical methods (Rivlin).

Sommaire:
Error estimate in pade approximation.- Orthogonal polynomials in monotone and convex interpolation.- Polynomials orthogonal with respect to singular continuous measures.- Group theoretic interpretations of Askey's scheme of hypergeometric orthogonal polynomials.- A review of orthogonal polynomials satisfying boundary value problems.- Orthogonal polynomial solutions to ordinary and partial differential equations.- Rational approximations, orthogonal polynomials and equilibrium distributions.- Factorization of second order difference equations and its application to orthogonal polynomials.- Gauss quadrature for analytic functions.- On the Geronimus polynomial sets.- The bounds for the error term of an asymptotic approximation of Jacobi polynomials.- The distribution of zeros of the polynomial eigenfunctions of ordinary differential operators of arbitrary order.- Orthogonal polynomials and jump modifications.- Electrostatic interpretation of zeros.- Associated dual Hahn polynomials.- Szego's Theorem for polynomials orthogonal with respect to varying measures.- Associated Askey-Wilson polynomials as Laguerre-Hahn orthogonal polynomials.- Le calcul des formes lineaires et les polyn?mes orthogonaux semi-classioues.- The Lp minimality and near-minimality of orthogonal polynomial approximation and integration methods.- Orthogonal rational functions with poles in a finite subset of R.- Nth-root asymptotics of orthonormal polynomials and non-diagonal pade approximants.- Zeros of orthogonal polynomials on harmonic algebraic curves.- Open problems.