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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
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.
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
Linking options:
https://www.mathnet.ru/eng/rm9786https://doi.org/10.1070/RM9786 https://www.mathnet.ru/eng/rm/v72/i4/p95
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Abstract page: | 909 | Russian version PDF: | 147 | English version PDF: | 27 | References: | 74 | First page: | 31 |
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