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Russian Mathematical Surveys, 2017, Volume 72, Issue 4, Pages 671–706
DOI: https://doi.org/10.1070/RM9786
(Mi rm9786)
 

This article is cited in 24 scientific papers (total in 25 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
References:
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.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant 14-50-00005.
Received: 14.07.2017
Russian version:
Uspekhi Matematicheskikh Nauk, 2017, Volume 72, Issue 4(436), Pages 95–130
DOI: https://doi.org/10.4213/rm9786
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: Primary 30F99, 41A21; Secondary 41A60
Language: English
Original paper language: Russian
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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\paper Hermite--Pad\'e approximants for meromorphic functions on a compact Riemann surface
\jour Uspekhi Mat. Nauk
\yr 2017
\vol 72
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\pages 95--130
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  • https://www.mathnet.ru/eng/rm/v72/i4/p95
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    References:74
    First page:31
     
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