# Multipoint Padé Approximants to Complex Cauchy Transforms with Polar Singularities

Abstract : We study diagonal multipoint Padé approximants to functions of the form $F(z) = \int\frac{d\mes(t)}{z-t}+R(z),$ where $R$ is a rational function and $\mes$ is a complex measure with compact regular support included in $\R$, whose argument has bounded variation on the support. Assuming that interpolation sets are such that their normalized counting measures converge sufficiently fast in the weak-star sense to some conjugate-symmetric distribution $\sigma$, we show that the counting measures of poles of the approximants converge to $\widehat\sigma$, the balayage of $\sigma$ onto the support of $\mes$, in the weak$^*$ sense, that the approximants themselves converge in capacity to $F$ outside the support of $\mes$, and that the poles of $R$ attract at least as many poles of the approximants as their multiplicity and not much more.
Keywords :
Type de document :
Article dans une revue
Journal of Approximation Theory, Elsevier, 2009, 156 (2), pp.187-211
Liste complète des métadonnées

Littérature citée [37 références]

https://hal.inria.fr/inria-00119160
Contributeur : Maxim Yattselev <>
Soumis le : lundi 2 août 2010 - 23:33:46
Dernière modification le : jeudi 11 janvier 2018 - 15:51:04
Document(s) archivé(s) le : jeudi 1 décembre 2016 - 11:22:58

### Fichier

BY1.pdf
Fichiers produits par l'(les) auteur(s)

### Identifiants

• HAL Id : inria-00119160, version 2

### Citation

Laurent Baratchart, Maxim Yattselev. Multipoint Padé Approximants to Complex Cauchy Transforms with Polar Singularities. Journal of Approximation Theory, Elsevier, 2009, 156 (2), pp.187-211. 〈inria-00119160v2〉

### Métriques

Consultations de la notice

## 355

Téléchargements de fichiers