Orthogonal rational functions on the real half line with poles in [-∞, 0]

Authors:
A. Bultheel;P. González-Vera;E. Hendriksen;O. Njåstad
Affiliations:
Department of Computer Science, K.U. Leuven, Celestijnenlaan 200 A, Leuven 3001, Belgium;Department Análisis Math., Univ. La Laguna, Tenerife, Spain;Department of Mathematics, University of Amsterdam, The Netherlands;Department of Mathematical Science, Norwegian University of Science and Technology, Trondheim, Norway
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
Year:
2005

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Abstract

The main objective is to generalize previous results obtained for orthogonal Laurent polynomials and their application in the context of Stieltjes moment problems to the multipoint case. The measure of orthogonality is supposed to have support on [0, ∞) while the orthogonal rational functions will have poles that are assumed to be "in the neighborhood of 0 and ∞". In this way orthogonal Laurent polynomials will be a special case obtained when all the poles are at 0 and ∞. We shall introduce the restrictions on the measure and the locations of the poles gradually and derive recurrence relations, Christoffel-Darboux relations, and the solution of the rational Stieltjes moment problem under appropriate conditions.