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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
\Bibitem{Gon74} \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 \mathnet{http://mi.mathnet.ru/msb3681} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=352477} \zmath{https://zbmath.org/?q=an:0304.30027} \transl \jour Math. USSR-Sb. \yr 1974 \vol 23 \issue 2 \pages 254--270 \crossref{https://doi.org/10.1070/SM1974v023n02ABEH002178} 

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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. 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
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
3. A. A. Gonchar, “On the speed of rational approximation of some analytic functions”, Math. USSR-Sb., 34:2 (1978), 131–145
4. N. S. Vyacheslavov, “On the approximation of $x^\alpha$ by rational functions”, Math. USSR-Izv., 16:1 (1981), 83–101
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
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
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
8. H. Stahl, “Best uniform rational approximation of $|x|$ on $[-1,1]$”, Russian Acad. Sci. Sb. Math., 76:2 (1993), 461–487
9. Stahl H., “Best Uniform Rational Approximation of X-Alpha on [0, 1]”, Bull. Amer. Math. Soc., 28:1 (1993), 116–122
10. Biancamaria Della Vecchia, Giuseppe Mastroianni, “Rational approximation in uniform and weighted L1 norm”, Journal of Computational and Applied Mathematics, 53:3 (1994), 333
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
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
13. A. I. Aptekarev, “Sharp constants for rational approximations of analytic functions”, Sb. Math., 193:1 (2002), 1–72
14. A. A. Gonchar, “Rational Approximations of Analytic Functions”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S44–S57
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
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
17. A. I. Aptekarev, “Integriruemye poludiskretizatsii giperbolicheskikh uravnenii – “skhemnaya” dispersiya i mnogomernaya perspektiva”, Preprinty IPM im. M. V. Keldysha, 2012, 020, 28 pp.
18. Hans-Peter Blatt, “Exact Maximal Convergence in Capacity and Zero Distribution of Rational Approximants”, Comput. Methods Funct. Theory, 2015
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
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