On Padé approximants of Markov-type meromorphic functions (Q2446982)

From the abstract: The paper is devoted to the asymptotic properties of diagonal Padé approximants for Markov-type meromorphic functions. The main result consists in strong asymptotic formulas for the denominators of diagonal Padé approximants for Markov-type meromorphic functions \(f=\widehat{\sigma}+r\) under additional constraints on the measure \(\sigma\) (\(r\) is a rational function). On the basis of these formulas, it is proved that, in a sufficiently small neighborhood of a pole of multiplicity \(m\) of such a meromorphic function \(f\), all poles of the diagonal Padé approximants \(f_n\) are simple and asymptotically located at the vertices of a regular \(m\)-gon.