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arXiv · 2106.01047

Tschebyshev-Pad\'e approximations for multivalued functions

Evguenii A. Rakhmanov·Sergey P. Suetin
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Abstract

We discuss the relation between the linear Tschebyshev-Pad\'e approximations to analytic function $f$ and the diagonal type I Hermite-Pad\'e polynomials for the tuple of functions $[1,f_1,f_2]$ where the pair of functions $f_1,f_2$ forms certain Nikishin system. An approach is proposed of how to extend the seminal Stahl's Theory for Pad\'e approximations for multivalued analytic functions to the Tschebyshev-Pad\'e approximations. The approach is based on the relation between Tschebyshev-Pad\'e approximations and Hermite-Pad\'e polynomials and also on a connection of Hermite-Pad\'e polynomials and multipoint Pad\'e approximants.

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Evguenii A. Rakhmanov, Sergey P. Suetin. 2021-06-02. Tschebyshev-Pad\'e approximations for multivalued functions. https://arxiv.org/abs/2106.01047

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