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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)

- Jan A Gorter, Erwin A Van Vliet, Han Rauwerda, Timo Breit, Robert Stad, Linda van Schaik +6 others
- Epilepsia
- 2007

We investigated expression of genes involved in the proteolytic process during epileptogenesis in a rat model of temporal lobe epilepsy (TLE). In a previous microarray study we found prominent activation of this process, which reached highest expression during the acute and latent phase (1 week after SE) in CA3 and entorhinal cortex (EC). Detailed analysis… (More)

- Adhemar Bultheel, Pablo Gonzz Alez-Vera, Erik Hendriksen, Olav Nj, N Katholieke, Universiteit Leuven
- 1990

We shall consider nested spaces L n , n = 0; 1; 2; : : : of rational functions with n prescribed poles outside the unit disk of the complex plane. We study orthogonal basis functions of these spaces for a general positive real measure on the unit circle. In the special case where all poles are placed at innnity, L n = n , the polynomials of degree at most… (More)

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)