This volume contains invited lectures and selected contributions from the International Workshop on Orthogonal Polynomials and Approximation Theory, held at Universidad Carlos III de Madrid on September 8-12, 2008, and which honored Guillermo López Lagomasino on his 60th birthday.

This book presents the state of the art in the theory of Orthogonal Polynomials and Rational Approximation with a special emphasis on their applications in random matrices, integrable systems, and numerical quadrature. New results and methods are presented in the papers as well as a careful choice of open problems, which can foster interest in research in these mathematical areas. This volume also includes a brief account of the scientific contributions by Guillermo López Lagomasino.

Readership

Graduate students and research mathematicians interested in orthogonal polynomials, approximation theory, and their applications.

Table of Contents

• F. Marcellán and A. Martínez-Finkelshtein -- Guillermo López Lagomasino: mathematical life
• B. de la Calle Ysern -- A walk through approximation theory
• L. Baratchart and M. Yattselev -- Asymptotic uniqueness of best rational approximants to complex Cauchy transforms in $L^2$ of the circle
• L. Garza and F. Marcellán -- Quadrature rules on the unit circle. A survey.
• A. Ibort, P. Linares, and J. G. Llavona -- On the multilinear trigonometric problem of moments
• A. B. J. Kuijlaars -- Multiple orthogonal polynomial ensembles
• E. Levin and D. S. Lubinsky -- Some equivalent formulations of universality limits in the bulk
• A. López García -- Greedy energy points with external fields
• A. Martínez-Finkelshtein and E. A. Rakhmanov -- On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials
• E. B. Saff -- Remarks on relative asymptotics for general orthogonal polynomials
• B. Simon -- Fine structure of the zeros of orthogonal polynomials: a progress report
• H. Stahl -- A potential-theoretic problem connected with complex orthogonality
• W. Van Assche -- Orthogonal polynomials and approximation theory: some open problems