Orthogonal Polynomials and their Applications

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 & López) and its relationship with other fields such as group theory (Koornwinder), Padé approximation (Brezinski), differential equations (Krall, Littlejohn) and numerical methods (Rivlin).

Autorentext
Francisco J. Marcellán is full professor of applied mathematics at the Universidad Carlos III de Madrid in Leganés (Spain) where he served as vice rector of research. In the past he has been teaching at the universities of Zaragoza, Santiago de Compostela and the Polytécnica de Madrid and was recently a visiting professor at the Georgia Institute of Technology. He was program director of the SIAM activity group on Orthogonal Polynomials and Special Functions from 1999 to 2005. Presently he is the director of the Spanish National Agency for Quality Assurance and Accreditation (ANECA). He has several publications in mathematical analysis (most particularly special functions and approximation) and linear algebra.
Walter Van Assche is full professor of mathematics at the Katholieke Universiteit Leuven in Belgium and was a research director of the Belgian National Fund for Scientific Research. He was vice chair of the SIAM activity group on Orthogonal Polynomials and Special Functions from 1999-2005 and is on the editorial board of the Journal of Approximation Theory and the Journal of Difference Equations and Applications.

Inhalt
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 polynômes 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.