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Mat. Sb. (N.S.), 1973, Volume 92(134), Number 1(9), Pages 152–164 (Mi msb3337)  

This article is cited in 15 scientific papers (total in 16 papers)

On the convergence of Padé approximants

A. A. Gonchar


Abstract: It is shown that if a function $f$ analytic at zero is similar to the rational functions ($f\in R^0$), the corresponding diagonal Padé sequence $\{\pi_n\}$ converges to $f$ in capacity inside of its natural domain of existence $W_f$.
Bibliography: 15 titles.

Full text: PDF file (1310 kB)
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English version:
Mathematics of the USSR-Sbornik, 1973, 21:1, 155–166

Bibliographic databases:

UDC: 517.53
MSC: 30A82, 30A22
Received: 22.03.1973

Citation: A. A. Gonchar, “On the convergence of Padé approximants”, Mat. Sb. (N.S.), 92(134):1(9) (1973), 152–164; Math. USSR-Sb., 21:1 (1973), 155–166

Citation in format AMSBIB
\Bibitem{Gon73}
\by A.~A.~Gonchar
\paper On~the convergence of Pad\'e approximants
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 92(134)
\issue 1(9)
\pages 152--164
\mathnet{http://mi.mathnet.ru/msb3337}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=325981}
\zmath{https://zbmath.org/?q=an:0287.30035}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 21
\issue 1
\pages 155--166
\crossref{https://doi.org/10.1070/SM1973v021n01ABEH002010}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Gonchar, “A local condition for the single-valuedness of analytic functions of several variables”, Math. USSR-Sb., 22:2 (1974), 305–322  mathnet  crossref  mathscinet  zmath
    2. A. A. Gonchar, “The rate of rational approximation and the property of single-valuedness of an analytic function in the neighborhood of an isolated singular point”, Math. USSR-Sb., 23:2 (1974), 254–270  mathnet  crossref  mathscinet  zmath
    3. A. A. Gonchar, “On the convergence of generalized Padé approximants of meromorphic functions”, Math. USSR-Sb., 27:4 (1975), 503–514  mathnet  crossref  mathscinet  zmath
    4. V. V. Vavilov, “On the convergence of the Padé approximants of meromorphic functions”, Math. USSR-Sb., 30:1 (1976), 39–49  mathnet  crossref  mathscinet  zmath  isi
    5. A. A. Gonchar, K. N. Lungu, “Poles of diagonal Padé approximants and the analytic continuation of functions”, Math. USSR-Sb., 39:2 (1981), 255–266  mathnet  crossref  mathscinet  zmath  isi
    6. E. A. Rakhmanov, “On the convergence of Padé approximants in classes of holomorphic functions”, Math. USSR-Sb., 40:2 (1981), 149–155  mathnet  crossref  mathscinet  zmath  isi
    7. A. S. Sadullaev, “Rational approximation and pluripolar sets”, Math. USSR-Sb., 47:1 (1984), 91–113  mathnet  crossref  mathscinet  zmath
    8. A. S. Sadullaev, “A criterion for rapid rational approximation in $\mathbf C^n$”, Math. USSR-Sb., 53:1 (1986), 271–281  mathnet  crossref  mathscinet  zmath
    9. F Wielonsky, “Rational Approximation to the Exponential Function with Complex Conjugate Interpolation Points”, Journal of Approximation Theory, 111:2 (2001), 344  crossref
    10. A. A. Bolibrukh, A. G. Vitushkin, V. S. Vladimirov, E. F. Mishchenko, S. P. Novikov, Yu. S. Osipov, A. G. Sergeev, P. L. Ul'yanov, L. D. Faddeev, E. M. Chirka, “Andrei Aleksandrovich Gonchar (on his 70th birthday)”, Russian Math. Surveys, 57:1 (2002), 191–198  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    11. A. A. Gonchar, “Rational Approximations of Analytic Functions”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S44–S57  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. 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
    13. Martinez-Finkelshtein A., Rakhmanov E.A., Suetin S.P., “Heine, Hilbert, Pade, Riemann, and Stieltjes: John Nuttall's Work 25 Years Later”, Recent Advances in Orthogonal Polynomials, Special Functions, and their Applications, Contemporary Mathematics, 578, eds. Arvesu J., Lagomasino G., Amer Mathematical Soc, 2011, 165–193  crossref  isi
    14. V. E. Vishnevskii, A. V. Zubov, O. A. Ivanova, “Approksimatsiya Pade resheniya zadachi Koshi”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 2012, no. 4, 3–17  mathnet
    15. Martinez-Finkelshtein A., Rakhmanov E.A., “Do Orthogonal Polynomials Dream of Symmetric Curves?”, Found. Comput. Math., 16:6 (2016), 1697–1736  crossref  isi
    16. A. Sadullaev, Z. Ibragimov, “The class $R$ and finely analytic functions”, Sb. Math., 209:8 (2018), 1234–1247  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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