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Sovrem. Probl. Mat., 2004, Issue 5, Pages 3–67
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This article is cited in 10 scientific papers (total in 11 papers)
On Padé Approximants of Meromorphic Functions of Markov Type
A. A. Gonchar, S. P. Suetin
Abstract:
The paper is devoted to the asymptotic properties of diagonal Padé approximants for Markov-type meromorphic functions. The main result is 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.
DOI:
https://doi.org/10.4213/spm8
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 272, suppl. 2, S58–S95
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UDC:
517.53
Citation:
A. A. Gonchar, S. P. Suetin, “On Padé Approximants of Meromorphic Functions of Markov Type”, Sovrem. Probl. Mat., 5, Steklov Math. Institute of RAS, Moscow, 2004, 3–67; Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S58–S95
Citation in format AMSBIB
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\vol 5
\pages 3--67
\publ Steklov Math. Institute of RAS
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\jour Proc. Steklov Inst. Math.
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http://mi.mathnet.ru/eng/spm8https://doi.org/10.4213/spm8 http://mi.mathnet.ru/eng/spm/v5/p3
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S. P. Suetin, “Strong asymptotics of zeros of polynomials orthogonal with respect to a complex-valued weight”, Russian Math. Surveys, 62:4 (2007), 823–825
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L. A. Knizhnerman, “Gauss–Arnoldi quadrature for $\langle(zI-A)^{-1}\varphi,\varphi\rangle$ and rational Padé-type approximation for Markov-type functions”, Sb. Math., 199:2 (2008), 185–206
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S. P. Suetin, “Strong asymptotics of polynomials orthogonal with respect to
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Alphonse P. Magnus, “Elliptic Hypergeometric Solutions to Elliptic Difference Equations”, SIGMA, 5 (2009), 038, 12 pp.
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V. A. Kalyagin, A. A. Kononova, “On Compact Perturbations of the Limit-Periodic Jacobi Operator”, Math. Notes, 86:6 (2009), 789–800
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A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Padé approximants, continued fractions, and orthogonal polynomials”, Russian Math. Surveys, 66:6 (2011), 1049–1131
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A. I. Aptekarev, G. López Lagomasino, E. B. Saff, V. Totik, H. Stahl, “Andrei Aleksandrovich Gonchar (on his 80th birthday)”, Russian Math. Surveys, 66:6 (2011), 1209–1216
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N. R. Ikonomov, R. K. Kovacheva, S. P. Suetin, “Nuttall's integral equation and Bernshtein's asymptotic formula for a complex weight”, Izv. Math., 79:6 (2015), 1215–1234
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