Multipoint Pade approximants to complex Cauchy transforms with polar singularities

JOURNAL OF APPROXIMATION THEORY

卷:156

Article

Baratchart, Laurent¹  Yattselev, Maxim¹ 

[1] INRIA, Project APICS, F-06902 Sophia Antipolis, France

关键词: Pade approximation;    Rational approximation;    Orthogonal polynomials;    Non-Hermitian orthogonality;   

DOI  :  10.1016/j.jat.2008.04.013

来源: Elsevier

【 摘 要 】

We study diagonal multipoint Pade approximants to functions of the form F(z) = integral d lambda(t)/z - t + R(z), where R is a rational function and lambda is a complex measure with compact regular Support included in R, whose argument has bounded variation oil the support. Assuming that interpolation sets are Such that their normalized counting measures converge sufficiently fast in the weak-star sense to sonic conjugate-symmetric distribution sigma, we show that the counting measures of poles of the approximants converge to (sigma) over cap, the balayage of sigma onto the support of lambda in the weak* sense, that the approximants themselves converge in capacity to F outside the support of lambda, and that the poles of R attract at least as many poles of the approximants as their multiplicity and not Much more. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free