Erik Hendriksen

Learn More
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)
Three cohort studies in adults were performed during the period from 1986 to 1989. Eight hundred and eighty-four subjects were, one or more times, immunized with influenza vaccines, and pre- and post-vaccination antibody titres were determined by hemagglutination inhibition tests. One thousand and one hundred and nineteen vaccination events in 681 subjects(More)
Cystatin C (CSTC), a cysteine protease inhibitor, has been implicated in the processes of neuronal degeneration and repair of the nervous system. Using serial analysis of gene expression (SAGE), we recently identified CSTC as one of the genes that are overexpressed after electrically induced status epilepticus (SE). In the present study, Western blot(More)
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)
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)
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 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)