# On Uniform Approximation of Rational Perturbations of Cauchy Integrals - Mathematics > Classical Analysis and ODEs

On Uniform Approximation of Rational Perturbations of Cauchy Integrals - Mathematics > Classical Analysis and ODEs - Download this document for free, or read online. Document in PDF available to download.

Abstract: We study AAK as well as Pad\-e approximants to functions f, where f is a sumof a Cauchy transform of a complex measure \mu supported on a real intervalincluded in -1,1, whose Radon-Nikodym derivative with respect to the arcsinedistribution on its support is Dini-continuous, non-vanishing and with andargument of bounded variation, and of a rational function with no poles on thesupport of \mu. It is shown that the approximants converge to f locallyuniformly in the domain of holomorphy of f, intersected with the unit disk inthe case of AAK approximants. In the case of Pad\-e approximants we need toassume that the interpolation scheme is -nearly- conjugate-symmetric.

Author: Maxim Yattselev

Source: https://arxiv.org/