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 Journal of Approximation Theory 156, 2 (2009) 187-211
 Available versions v1 (2006-12-08) v2 (2010-08-03)
 Multipoint Padé Approximants to Complex Cauchy Transforms with Polar Singularities
 (2009)
 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.
 1: APICS (INRIA Sophia Antipolis) INRIA
 Domain : Mathematics/Classical Analysis and ODEs
 Keywords: Rational approximation – Padé approximation – Orthogonal polynomials.
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 inria-00119160, version 2 http://hal.inria.fr/inria-00119160 oai:hal.inria.fr:inria-00119160 From: Maxim Yattselev <> Submitted on: Monday, 2 August 2010 23:33:46 Updated on: Tuesday, 3 August 2010 12:53:38