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Mat. Sb. (N.S.), 1981, Volume 115(157), Number 4(8), Pages 590–613 (Mi msb2424)  

This article is cited in 39 scientific papers (total in 40 papers)

Poles of rows of the Padé table and meromorphic continuation of functions

A. A. Gonchar


Abstract: The meromorphic continuation of a function is characterized in terms of the asymptotic behavior of the poles of its local rational approximations (rows of the Padé table).
Bibliography: 15 titles.

Full text: PDF file (2255 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1982, 43:4, 527–546

Bibliographic databases:

UDC: 517.53
MSC: 30B40, 30E10, 30D30
Received: 03.02.1981

Citation: A. A. Gonchar, “Poles of rows of the Padé table and meromorphic continuation of functions”, Mat. Sb. (N.S.), 115(157):4(8) (1981), 590–613; Math. USSR-Sb., 43:4 (1982), 527–546

Citation in format AMSBIB
\Bibitem{Gon81}
\by A.~A.~Gonchar
\paper Poles of rows of the Pad\'e table and meromorphic continuation of functions
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 115(157)
\issue 4(8)
\pages 590--613
\mathnet{http://mi.mathnet.ru/msb2424}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=629629}
\zmath{https://zbmath.org/?q=an:0492.30020|0477.30021}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 43
\issue 4
\pages 527--546
\crossref{https://doi.org/10.1070/SM1982v043n04ABEH002579}


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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. A. A. Gonchar, “On uniform convergence of diagonal Padé approximants”, Math. USSR-Sb., 46:4 (1983), 539–559  mathnet  crossref  mathscinet  zmath  isi
    2. V. I. Buslaev, “On the poles of the $m$th row of the Padé table”, Math. USSR-Sb., 45:4 (1983), 423–429  mathnet  crossref  mathscinet  zmath  isi
    3. S. P. Suetin, “On poles of the $m$th row of a Padé table”, Math. USSR-Sb., 48:2 (1984), 493–497  mathnet  crossref  mathscinet  zmath  isi
    4. V. I. Buslaev, A. A. Gonchar, S. P. Suetin, “On convergence of subsequences of the $m$th row of a Padé table”, Math. USSR-Sb., 48:2 (1984), 535–540  mathnet  crossref  mathscinet  zmath  isi
    5. V. V. Vavilov, V. A. Prokhorov, S. P. Suetin, “The poles of the $m$th row of the Padé table and the singular points of a function”, Math. USSR-Sb., 50:2 (1985), 457–463  mathnet  crossref  mathscinet  zmath  isi
    6. S. P. Suetin, “On an inverse problem for the $m$th row of a Padé table”, Math. USSR-Sb., 52:1 (1985), 231–244  mathnet  crossref  mathscinet  zmath  isi
    7. Prokhorov V., “Tschebyschev Rational-Approximations of Analytic-Functions”, 276, no. 6, 1984, 1321–1324  mathscinet  zmath  isi
    8. Lagomasino G. Vavilov V., “Survey on Recent Advances in Inverse Problems of Pade-Approximation Theory”, 1105, 1984, 11–26  mathscinet  zmath  isi
    9. V. I. Buslaev, “Relations for the coefficients, and singular points of a function”, Math. USSR-Sb., 59:2 (1988), 349–377  mathnet  crossref  mathscinet  zmath  isi
    10. Chin L., “On the M-Th Row of the Table of Multipoint Pade Approximations”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1987, no. 3, 50–53  zmath  isi
    11. V. A. Prokhorov, “The poles of Tchebycheff rational approximations and meromorphic extension of functions”, Math. USSR-Sb., 69:2 (1991), 379–391  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. Le ba Kkhan' Chin', “Inverse theorems for multipoint Padé approximants”, Math. USSR-Sb., 71:1 (1992), 149–161  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. Koshel S., Chekryzhov S., “On Approximate Values of Analytic-Functions Zeros”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1990, no. 5, 8–12  mathscinet  isi
    14. Gravesmorris P. Saff E., “Divergence of Vector-Valued Rational Interpolants to Meromorphic Functions”, Rocky Mt. J. Math., 21:1 (1991), 245–261  crossref  mathscinet  isi
    15. D. Barrios, G. L. Lopes, E. Torrano, “Zeros and asymptotics of polynomials satisfying three-term recurrence relations with complex coefficients”, Russian Acad. Sci. Sb. Math., 80:2 (1995), 309–333  mathnet  crossref  mathscinet  zmath  isi
    16. D. Barrios, G. L. Lopes, E. Torrano, “Polynomials generated by a three-term recurrence relation with asymptotically periodic complex coefficients”, Sb. Math., 186:5 (1995), 629–659  mathnet  crossref  mathscinet  zmath  isi
    17. A.Fernández Infante, G.López Lagomasino, “Overconvergence of subsequences of rows of Padé approximants with gaps”, Journal of Computational and Applied Mathematics, 105:1-2 (1999), 265  crossref
    18. S. P. Suetin, “Padé approximants and efficient analytic continuation of a power series”, Russian Math. Surveys, 57:1 (2002), 43–141  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    19. 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
    20. A. A. Gonchar, “Rational Approximations of Analytic Functions”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S44–S57  mathnet  crossref  crossref  mathscinet  zmath  isi
    21. S. L. Skorokhodov, “Padé approximation and numerical analysis for the Riemann $\zeta$-function”, Comput. Math. Math. Phys., 43:9 (2003), 1277–1298  mathnet  mathscinet  zmath
    22. Adukov V., “The Uniform Convergence of Subsequences of the Last Intermediate Row of the Pade Table”, J. Approx. Theory, 122:2 (2003), 160–207  crossref  mathscinet  zmath  isi
    23. S. L. Skorokhodov, “Methods of analytical continuation of the generalized hypergeometric functions $ _pF_{p-1}(a_1,…,a_p;b_1,…,b_{p-1};z)$”, Comput. Math. Math. Phys., 44:7 (2004), 1102–1123  mathnet  mathscinet  zmath
    24. V. I. Buslaev, S. F. Buslaeva, “Poincare Theorem for Difference Equations”, Math. Notes, 78:6 (2005), 877–882  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    25. V. I. Buslaev, “On the Fabry Ratio Theorem for Orthogonal Series”, Proc. Steklov Inst. Math., 253 (2006), 8–21  mathnet  crossref  mathscinet  elib
    26. D. V. Khristoforov, “On Asymptotic Properties of Interpolation Polynomials”, Math. Notes, 83:1 (2008), 116–124  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    27. Laurent Baratchart, Maxim Yattselev, “Convergent Interpolation to Cauchy Integrals over Analytic Arcs”, Found Comput Math, 2009  crossref  isi
    28. V. I. Buslaev, “An analogue of Fabry's theorem for generalized Padé approximants”, Sb. Math., 200:7 (2009), 981–1050  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    29. S. P. Suetin, “Numerical Analysis of Some Characteristics of the Limit Cycle of the Free van der Pol Equation”, Proc. Steklov Inst. Math., 278, suppl. 1 (2012), S1–S54  mathnet  crossref  crossref  isi  elib
    30. 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
    31. J. Cacoq, B. de la Calle Ysern, G. López Lagomasino, “Incomplete Padé approximation and convergence of row sequences of Hermite–Padé approximants”, Journal of Approximation Theory, 2012  crossref
    32. G. Henkin, V. Michel, “Inverse Dirichlet-to-Neumann problem for nodal curves”, Russian Math. Surveys, 67:6 (2012), 1069–1089  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    33. M. Bello Hernández, B. de la Calle Ysern, “Meromorphic continuation of functions and arbitrary distribution of interpolation points”, Journal of Mathematical Analysis and Applications, 2013  crossref
    34. J. Cacoq, B. Calle Ysern, G. López Lagomasino, “Direct and Inverse Results on Row Sequences of Hermite–Padé Approximants”, Constr Approx, 2013  crossref
    35. B. d.l.a.C.alle Ysern, J. Mínguez Ceniceros, “Rate of convergence of row sequences of multipoint Padé approximants”, Journal of Computational and Applied Mathematics, 2014  crossref
    36. Yattselev M.L., “Nuttall's Theorem With Analytic Weights on Algebraic S-Contours”, J. Approx. Theory, 190:SI (2015), 73–90  crossref  isi
    37. G. López Lagomasino, Y. Zaldivar Gerpe, “Inverse Results on Row Sequences of Hermite–Padé Approximation”, Proc. Steklov Inst. Math., 298 (2017), 152–169  mathnet  crossref  crossref  isi  elib
    38. N. Bosuwan, “Convergence of Row Sequences of Simultaneous Padé–Faber Approximants”, Math. Notes, 103:5 (2018), 683–693  mathnet  crossref  crossref  isi  elib
    39. Bosuwan N., “Direct and Inverse Results on Row Sequences of Generalized Pade Approximants to Polynomial Expansions”, Acta Math. Hung., 157:1 (2019), 191–219  crossref  mathscinet  isi  scopus
    40. Bosuwan N. Lopez Lagomasino G., “Direct and Inverse Results on Row Sequences of Simultaneous Pade-Faber Approximants”, Mediterr. J. Math., 16:2 (2019), 36  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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