A weak-star convergence result for orthogonal rational functions

Authors:
J. Van Deun;A. Bultheel
Affiliations:
Department of Computer Science, Katholieke University Leuven, Celestijnenlaan 200A, Heverlee 3001, Belgium;Department of Computer Science, K.U. Leuven, Belgium
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications
Year:
2005

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Abstract

We prove a weak-star convergence result for orthogonal rational functions on the interval [-1, 1] which generalizes a well-known result by Rakhmanov (Math. USSR-Sb. 32(1977) 199). As an application, we use this result to aooroximate a certain integral which occurs in the computation of orthogonal rational functions.