On $L_{\mathbb R}^2$-best rational approximants to Markov functions on several intervals

Maxim L. Yattselev

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arXiv · 2202.00800

On $L_{\mathbb R}^2$-best rational approximants to Markov functions on several intervals

Maxim L. Yattselev

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Abstract

Let $ f(z)=\int(z-x)^{-1}d\mu(x) $, where $ \mu $ is a Borel measure supported on several subintervals of $ (-1,1) $ with smooth Radon-Nikodym derivative. We study strong asymptotic behavior of the error of approximation $ (f-r_n)(z) $, where $ r_n(z) $ is the $ L_{\mathbb R}^2$-best rational approximant to $ f(z) $ on the unit circle with $ n $ poles inside the unit disk.

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BibTeX RIS

Maxim L. Yattselev. 2022-02-01. On $L_{\mathbb R}^2$-best rational approximants to Markov functions on several intervals. https://arxiv.org/abs/2202.00800

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