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Sovrem. Probl. Mat., 2004, Issue 5, Pages 3–67 (Mi spm8)  

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

Bibliographic databases:

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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\paper On Pad\'e Approximants of Meromorphic Functions of Markov Type
\serial Sovrem. Probl. Mat.
\yr 2004
\vol 5
\pages 3--67
\publ Steklov Math. Institute of RAS
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
\yr 2011
\vol 272
\issue , suppl. 2
\pages S58--S95
\crossref{https://doi.org/10.1134/S0081543811030059}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. P. Suetin, “Spectral properties of a class of discrete Sturm–Liouville operators”, Russian Math. Surveys, 61:2 (2006), 365–367  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. S. P. Suetin, “Comparative Asymptotic Behavior of Solutions and Trace Formulas for a Class of Difference Equations”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S96–S137  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. S. P. Suetin, “Trace formulae for a class of Jacobi operators”, Sb. Math., 198:6 (2007), 857–885  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. S. P. Suetin, “Strong asymptotics of polynomials orthogonal with respect to a complex weight”, Sb. Math., 200:1 (2009), 77–93  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. Alphonse P. Magnus, “Elliptic Hypergeometric Solutions to Elliptic Difference Equations”, SIGMA, 5 (2009), 038, 12 pp.  mathnet  crossref  mathscinet  zmath
    8. V. A. Kalyagin, A. A. Kononova, “On Compact Perturbations of the Limit-Periodic Jacobi Operator”, Math. Notes, 86:6 (2009), 789–800  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
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