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- Adhemar Bultheel, Pablo González-Vera, Erik Hendriksen, Olav Njåstad
- Cambridge monographs on applied and computational…
- 2009

Introduction This monograph forms an introduction to the theory of orthogonal rational functions. The simplest way to see what we mean by orthogonal rational functions is to consider them as generalizations of orthogonal polynomials. There is not much confusion about the meaning of an orthogonal polynomial sequence. One says that f n g 1 n=0 is an… (More)

- A Bultheel, P Gonzz Alez-Vera, E Hendriksen, O Nj Astad Received
- 1998

Let R be the space of rational functions with poles among f k ; 1= k g 1 k=0 with 0 = 0 and j k j < 1, k 1. We consider a sequence fR n g 1 n=0 of nested subspaces with 1 n=0 R n = R. We continue our investigation of the convergence as n ! 1 of quadrature rules which are exact in R n. In Part II we have discussed the convergence for a particular nesting of… (More)

- Adhemar Bultheel, Pablo González-Vera, Erik Hendriksen, Olav Njåstad
- Numerical Algorithms
- 1992

In this paper we shall be concerned with the problem of approximating the integralI μ{f}=∫ −π π f(eiθ) dμ(θ), by means of the formulaI n {f}=Σ j=1 n A j (n) f(x j (n) ) where μ is some finite positive measure. We want the approximation to be so thatI n{f}=I μ{f} forf belonging to certain classes of rational functions with prescribed poles which generalize… (More)

- A Bultheel, P Gonzz Alez-Vera, E Hendriksen, O Nj Astad Received
- 1998

Let R be the space of rational functions with poles among f k ; 1= k g 1 k=0 with 0 = 0 and j k j < 1, k 1. We consider a sequence fR n g 1 n=0 of nested subspaces with 1 n=0 R n = R. First we recall from part I how to nd orthogonal bases for R for a positive measure on the unit circle. These are used in the construction of interpolatory quadrature rules… (More)

- Adhemar Bultheel, Pablo González-Vera, Erik Hendriksen, Olav Njåstad
- Applied Mathematics and Computation
- 2002

- E M Hendriksen, P N Span, +4 authors J Bussink
- Microvascular research
- 2009

Tumour growth and spread of tumour cells requires angiogenesis. Incipient angiogenesis is not induced by tumour cell hypoxia but probably by proangiogenic factors. During growth tumours depend on a further induction of vascular development for adequate oxygen and nutrient supply. If the oxygen supply is insufficient, the resulting hypoxia stimulates… (More)

- Jan A Gorter, Erwin A Van Vliet, +9 authors Wytse J Wadman
- 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 González-Vera, Erik Hendriksen, Olav Njåstad
- J. Complexity
- 2003

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)

- Adhemar Bultheel, Pablo Gonz, Erik Hendriksen, Pablo Gonz alez-Vera
- 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)

- Adhemar Bultheel, Pablo González-Vera, Erik Hendriksen, Olav Njåstad
- J. Computational Applied Mathematics
- 2013

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)