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arXiv · 0909.0461

Asymptotic Uniqueness of Best Rational Approximants to Complex Cauchy Transforms in ${L}^2$ of the Circle

Laurent Baratchart·Maxim Yattselev
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Abstract

For all n large enough, we show uniqueness of a critical point in best rational approximation of degree n, in the L^2-sense on the unit circle, to functions f, where f is a sum of a Cauchy transform of a complex measure μsupported on a real interval included in (-1,1), whose Radon-Nikodym derivative with respect to the arcsine distribution on its support is Dini-continuous, non-vanishing and with and argument of bounded variation, and of a rational function with no poles on the support of μ.

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Laurent Baratchart, Maxim Yattselev. 2009-09-02. Asymptotic Uniqueness of Best Rational Approximants to Complex Cauchy Transforms in ${L}^2$ of the Circle. https://arxiv.org/abs/0909.0461

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