This article is cited in 27 papers

Hermite–Padé approximants for meromorphic functions on a compact Riemann surface

A. V. Komlov, R. V. Palvelev, S. P. Suetin, E. M. Chirka

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: The problem of the limiting distribution of the zeros and the asymptotic behaviour of the Hermite–Padé polynomials of the first kind is considered for a system of germs $[1,f_{1,\infty},\dots,f_{m,\infty}]$ of meromorphic functions $f_j$, $j=1,\dots,m$, on an $(m+1)$-sheeted Riemann surface ${\mathfrak R}$. Nuttall's approach to the solution of this problem, based on a particular ‘Nuttall’ partition of ${\mathfrak R}$ into sheets, is further developed.
Bibliography: 36 titles.

Keywords: rational approximants, Hermite–Padé polynomials, distribution of zeros, convergence in capacity.

UDC: 517.53

MSC: Primary 30F99, 41A21; Secondary 41A60

Received: 14.07.2017

DOI: 10.4213/rm9786

 English version: Russian Mathematical Surveys, 2017, 72:4, 671–706

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