Conference on Orthogonal Functions and Related Topics location:Roros, Norway date:August 12-16, 2003
The main objective is to generalize previous results obtained for orthogonal Laurent polynomials and in the context of Stieltjes moment problems to the multipoint case. The measure of orthogonality is supposed to have a support on [0,∞) while the orthogonal rational functions will have poles that are assumed to be "in the neighborhood of 0 and infinity". In this way orthogonal Laurent polynomials will be a special case obtained when all the poles are at 0 and infinity. 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.