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Mat. Sb. (N.S.), 1974, Volume 94(136), Number 2(6), Pages 265–282 (Mi msb3681)  

This article is cited in 18 scientific papers (total in 19 papers)

The rate of rational approximation and the property of single-valuedness of an analytic function in the neighborhood of an isolated singular point

A. A. Gonchar

Abstract: Criteria are obtained for the single-valuedness of an analytic function $\mathscr F$ in the neighborhood of an isolated singular point in terms of the rate of convergence of rational approximation to a fixed branch of the function $\mathscr F$.
Bibliography: 8 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 23:2, 254–270

Bibliographic databases:

UDC: 517.53
MSC: Primary 30A82; Secondary 30A44
Received: 04.11.1973

Citation: 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”, Mat. Sb. (N.S.), 94(136):2(6) (1974), 265–282; Math. USSR-Sb., 23:2 (1974), 254–270

Citation in format AMSBIB
\by A.~A.~Gonchar
\paper The rate of rational approximation and the property of single-valuedness of an analytic function in the neighborhood of an isolated singular point
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 94(136)
\issue 2(6)
\pages 265--282
\jour Math. USSR-Sb.
\yr 1974
\vol 23
\issue 2
\pages 254--270

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    This publication is cited in the following articles:
    1. L. D. Grigoryan, “Estimates of the norm of the holomorphic components of functions meromorphic in domains with a smooth boundary”, Math. USSR-Sb., 29:1 (1976), 139–146  mathnet  crossref  mathscinet  zmath  isi
    2. N. S. Vyacheslavov, “On the least deviations of the function $\operatorname{sign}x$ and its primitives from the rational functions in the $L_p$ metrics, $0<p\leqslant\infty$”, Math. USSR-Sb., 32:1 (1977), 19–31  mathnet  crossref  mathscinet  zmath  isi
    3. A. A. Gonchar, “On the speed of rational approximation of some analytic functions”, Math. USSR-Sb., 34:2 (1978), 131–145  mathnet  crossref  mathscinet  zmath  isi
    4. N. S. Vyacheslavov, “On the approximation of $x^\alpha$ by rational functions”, Math. USSR-Izv., 16:1 (1981), 83–101  mathnet  crossref  mathscinet  zmath  isi
    5. Ramazanov A., “Rings of the Coefficients of Rational Functions and Polynomials Best Approximating Functions Chi-Alpha”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1980, no. 5, 41–44  isi
    6. A. A. Pekarskii, “Tchebycheff rational approximation in the disk, on the circle, and on a closed interval”, Math. USSR-Sb., 61:1 (1988), 87–102  mathnet  crossref  mathscinet  zmath
    7. A. A. Gonchar, E. A. Rakhmanov, “Equilibrium distributions and degree of rational approximation of analytic functions”, Math. USSR-Sb., 62:2 (1989), 305–348  mathnet  crossref  mathscinet  zmath  isi
    8. H. Stahl, “Best uniform rational approximation of $|x|$ on $[-1,1]$”, Russian Acad. Sci. Sb. Math., 76:2 (1993), 461–487  mathnet  crossref  mathscinet  zmath  isi
    9. Stahl H., “Best Uniform Rational Approximation of X-Alpha on [0, 1]”, Bull. Amer. Math. Soc., 28:1 (1993), 116–122  crossref  isi
    10. Biancamaria Della Vecchia, Giuseppe Mastroianni, “Rational approximation in uniform and weighted L1 norm”, Journal of Computational and Applied Mathematics, 53:3 (1994), 333  crossref
    11. Saff E. Stahl H., “Ray Sequences of Best Rational Approximants for [X](Alpha)”, Can. J. Math.-J. Can. Math., 49:5 (1997), 1034–1065  crossref  isi
    12. 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
    13. A. I. Aptekarev, “Sharp constants for rational approximations of analytic functions”, Sb. Math., 193:1 (2002), 1–72  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. A. A. Gonchar, “Rational Approximations of Analytic Functions”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S44–S57  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. 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
    16. A. A. Pekarskii, “Approximation to the Function $z^{\alpha}$ by Rational Fractions in a Domain with Zero External Angle”, Math. Notes, 91:5 (2012), 714–724  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    17. A. I. Aptekarev, “Integriruemye poludiskretizatsii giperbolicheskikh uravnenii – “skhemnaya” dispersiya i mnogomernaya perspektiva”, Preprinty IPM im. M. V. Keldysha, 2012, 020, 28 pp.  mathnet
    18. Hans-Peter Blatt, “Exact Maximal Convergence in Capacity and Zero Distribution of Rational Approximants”, Comput. Methods Funct. Theory, 2015  crossref
    19. E. A. Rakhmanov, “The Gonchar-Stahl $\rho^2$-theorem and associated directions in the theory of rational approximations of analytic functions”, Sb. Math., 207:9 (2016), 1236–1266  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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