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In this paper we generalize the notion of orthogonal Laurent polynomials to orthogonal rational functions. Orthogonality is considered with respect to a measure on the positive real line. From this, Gauss-type quadrature formulas are derived and multipoint Padé approximants for the Stieltjes transform of the measure. Convergence of both the quadrature… (More)

We consider a positive measure on [0, ∞) and a sequence of nested spaces L 0 ⊂ L 1 ⊂ L 2 · · · of rational functions with prescribed poles in [−∞, 0]. Let {ϕ k } ∞ k=0 , with ϕ 0 ∈ L 0 and ϕ k ∈ L k \ L k−1 , k = 1, 2,. .. be the associated sequence of orthogonal rational functions. The zeros of ϕ n can be used as the nodes of a rational Gauss quadrature… (More)

We consider indeterminate rational moment problems on the real line with their associated orthogonal rational functions. There exists a Nevanlinna type parameterization relating to the problem, with associated Nevanlinna matrices of functions having singularities in the closure of the set of poles of the rational functions belonging to the problem. We prove… (More)

We consider rational moment problems on the real line with their associated orthogonal rational functions. There exists a Nevan-linna type parameterization relating to the problem, with associated Nevanlinna matrices of functions having singularities in the closure of the set of poles of the rational functions belonging to the problem. We prove results… (More)