Tschebyshev-Padé approximations for multivalued functions

Abstract

We discuss the relation between the linear Tschebyshev-Padé approximations to analytic function $f$ and the diagonal type I Hermite-Padé 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 Padé approximations for multivalued analytic functions to the Tschebyshev-Padé approximations. The approach is based on the relation between Tschebyshev-Padé approximations and Hermite-Padé polynomials and also on a connection of Hermite-Padé polynomials and multipoint Padé approximants.

20 pages