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TW 375
A. Bultheel, A. Cuyt, W. Van Assche, M. Van Barel, B. Verdonk
Generalizations of orthogonal polynomials
Abstract
We give a survey of recent generalizations for orthogonal polynomials that were recently obtained. It concerns not only multidimensional (matrix and vector orthogonal polynomials) and multivariate versions, or multipole (orthogonal rational functions) variants of the classical polynomials but also extensions of the orthogonality conditions (multiple orthogonality). Most of these generalizations are inspired by the applications in which they are applied. We also give a glimpse of the applications, but they are usually also generalizations of applications where classical orthogonal polynomials play a fundamental role: moment problems, numerical quadrature, rational approximation, linear algebra, recurrence relations, random matrices.
report.pdf / mailto: A. Bultheel