On the size of multivariate polynomial lemniscates and the convergence of rational approximants

In a previous paper, the author introduced a class of multivariate rational interpolants, which are called optimal Padé-type approximants (OPTA). The main goal of this paper is to extend classical results on convergence both in measure and in capacity of sequences of Padé approximants to the multiva...

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Veröffentlicht in:Journal of approximation theory Jg. 143; H. 2; S. 176 - 200
1. Verfasser: García, Zebenzuí
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.12.2006
Schlagworte:
Capacity
Convergence
Hausdorff content
Meromorphic functions in several variables
Multivariate Padé approximants
Multivariate Padé approximants
Hausdorff content
Capacity
Convergence
Meromorphic functions in several variables
ISSN:0021-9045, 1096-0430
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Zusammenfassung:In a previous paper, the author introduced a class of multivariate rational interpolants, which are called optimal Padé-type approximants (OPTA). The main goal of this paper is to extend classical results on convergence both in measure and in capacity of sequences of Padé approximants to the multivariate case using OPTA. To this end, we obtain some estimations of the size of multivariate polynomial lemniscates in terms of the Hausdorff content, which we also think are of some interest.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2006.04.003