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Uspekhi Mat. Nauk, 2017, Volume 72, Issue 4(436), Pages 95–130 (Mi umn9786)  

This article is cited in 11 scientific papers (total in 12 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 $[1,f_{1,\infty},…,f_{m,\infty}]$ of meromorphic functions $f_j$, $j=1,…,m$, 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.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/rm9786

Full text: PDF file (792 kB)
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English version:
Russian Mathematical Surveys, 2017, 72:4, 671–706

Bibliographic databases:

UDC: 517.53
MSC: Primary 30F99, 41A21; Secondary 41A60
Received: 14.07.2017

Citation: A. V. Komlov, R. V. Palvelev, S. P. Suetin, E. M. Chirka, “Hermite–Padé approximants for meromorphic functions on a compact Riemann surface”, Uspekhi Mat. Nauk, 72:4(436) (2017), 95–130; Russian Math. Surveys, 72:4 (2017), 671–706

Citation in format AMSBIB
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