Preface This volume contains articles by speakers in the International Workshop on Orthogonal Polynomials and Approximation Theory, held on September 8-12, 2008, at the Legan´ es campus of the Universidad Carlos III de Madrid, in honor of the 60th birthday of Professor Guillermo opez Lagomasino. The five-day conference attracted 140 participants from 22 countries. The program of the conference, video, and pdf files of most of the talks can be found at http://gama.uc3m.es. This volume’s articles cover a wide range of topics in the theory of Orthogonal Polynomials as well as in Rational Approximation with a special emphasis on their applications in random matrices, integrable systems, and numerical quadrature. The contributors are celebrated researchers in these domains. A brief account of the scientific contributions by Professor Guillermo L´opez Lagomasino constitutes one of the features of this volume. His activity in the for- mer Soviet Union, in the framework of the group lead by A. A. Gonchar, as well as their connections with the Western groups working in Orthogonal Polynomials and Approximation Theory, fulfils a good historical perspective of the internationaliza- tion of these domains in the last 50 years. This is an example of how mathematicians are able to open physical and political barriers and contribute to the improved links between individuals and institutions. New results and methods are presented in the contributed papers as well as a careful choice of open problems to foster an interest in research in these mathemati- cal areas in the coming years. The reader will find survey presentations, an account of recent developments, and the exposition of new trends in the areas of Orthogonal Polynomials, Special Functions, and Approximation Theory, from a theoretical and an applied perspectives. As co-organizers of the workshop and editors of this volume it is our happy task to thank those individuals and institutions whose efforts made it possible. First, we acknowledge Ministerio de Educaci´ on y Ciencia of Spain (grant MTM2007-31221- E), Proyecto Ingenio Mathematica (i-MATH)(grant C3-0116), Universidad Car- los III de Madrid, Universidad Polit´ ecnica de Madrid, Real Sociedad Matem´atica Espa˜ nola, Sociedad Espa˜ nola de Matem´ atica Aplicada, Ayuntamiento de Legan´es, and International Association for the promotion and cooperation with scientists (INTAS) for their financial support. Second, it is a pleasure to thank all the mem- bers of the local organization Committee of the Universidad Carlos III de Madrid for the excellent organization of this meeting. Last, but certainly not least, we ex- press our gratitude to the participants of the workshop who made it a memorable ix
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