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Mat. Sb. (N.S.), 1969, Volume 78(120), Number 4, Pages 640–654 (Mi msb3575)  

This article is cited in 51 scientific papers (total in 52 papers)

Zolotarev problems connected with rational functions

A. A. Gonchar


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English version:
Mathematics of the USSR-Sbornik, 1969, 7:4, 623–635

Bibliographic databases:

UDC: 517.53
MSC: 26C15, 26A12, 41A20
Received: 16.12.1968

Citation: A. A. Gonchar, “Zolotarev problems connected with rational functions”, Mat. Sb. (N.S.), 78(120):4 (1969), 640–654; Math. USSR-Sb., 7:4 (1969), 623–635

Citation in format AMSBIB
\Bibitem{Gon69}
\by A.~A.~Gonchar
\paper Zolotarev problems connected with rational functions
\jour Mat. Sb. (N.S.)
\yr 1969
\vol 78(120)
\issue 4
\pages 640--654
\mathnet{http://mi.mathnet.ru/msb3575}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=254238}
\zmath{https://zbmath.org/?q=an:0199.12801|0203.07302}
\transl
\jour Math. USSR-Sb.
\yr 1969
\vol 7
\issue 4
\pages 623--635
\crossref{https://doi.org/10.1070/SM1969v007n04ABEH001107}


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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 of single-valuedness of analytic functions”, Math. USSR-Sb., 18:1 (1972), 151–167  mathnet  crossref  mathscinet  zmath
    2. Dov Aharonov, Joseph L Walsh, “On the convergence of rational functions of best approximation to a meromorphic function”, Journal of Mathematical Analysis and Applications, 40:2 (1972), 418  crossref
    3. A. A. Gonchar, “On the convergence of Padé approximants”, Math. USSR-Sb., 21:1 (1973), 155–166  mathnet  crossref  mathscinet  zmath
    4. 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
    5. A. P. Bulanov, “Asymptotic behavior of the least deviations of the function $\operatorname{sgn}x$ from rational functions”, Math. USSR-Sb., 25:2 (1975), 159–176  mathnet  crossref  mathscinet  zmath
    6. 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
    7. 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
    8. Pekarskii A., “Rational-Approximations of Absolutely Continuous-Functions with a Derivative From the Orlich Space”, Dokl. Akad. Nauk Belarusi, 24:4 (1980), 301–304  isi
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    10. A. S. Sadullaev, “Plurisubharmonic measures and capacities on complex manifolds”, Russian Math. Surveys, 36:4 (1981), 61–119  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. A. A. Pekarskii, “Rational approximations of absolutely continuous functions with derivative in an Orlicz space”, Math. USSR-Sb., 45:1 (1983), 121–137  mathnet  crossref  mathscinet  zmath
    12. K. Yu. Osipenko, “Heins' problem and optimal extrapolation of analytic functions prescribed with an error”, Math. USSR-Sb., 54:2 (1986), 551–559  mathnet  crossref  mathscinet  zmath
    13. Vladov N., “Exact Asymptotics for the Rational Approximation of Sign(X) in Hausdorff Metric”, 39, no. 7, 1986, 37–40  isi
    14. Helmut Kloke, “Some inequalities for the capacity of plane condensers”, Results. Math, 9:1-2 (1986), 82  crossref
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    16. Gerhard Starke, “Optimal Alternating Direction Implicit Parameters for Nonsymmetric Systems of Linear Equations”, SIAM J Numer Anal, 28:5 (1991), 1431  crossref  mathscinet  zmath  isi
    17. A. L. Levin, E. B. Saff, “$L_p$ extensions of Gonchar's inequality for rational functions”, Russian Acad. Sci. Sb. Math., 76:1 (1993), 199–210  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    18. Gerhard Starke, “Near-circularity for the rational Zolotarev problem in the complex plane”, Journal of Approximation Theory, 70:1 (1992), 115  crossref
    19. N. Levenberg, L. Reichel, “A generalized ADI iterative method”, Numer Math, 66:1 (1993), 215  crossref  mathscinet  zmath  isi
    20. Gerhard Starke, “Fejér-Walsh points for rational functions and their use in the ADI iterative method”, Journal of Computational and Applied Mathematics, 46:1-2 (1993), 129  crossref
    21. M.-P. Istace, J.-P. Thiran, “On the Third and Fourth Zolotarev Problems in the Complex Plane”, SIAM J Numer Anal, 32:1 (1995), 249  crossref  mathscinet  zmath  isi
    22. B. Le Bailly, J. P. Thiran, “Optimal Rational Functions for the Generalized Zolotarev Problem in the Complex Plane”, SIAM J Numer Anal, 38:5 (2000), 1409  crossref  mathscinet  zmath  isi
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    24. 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
    25. A. A. Gonchar, “Rational Approximations of Analytic Functions”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S44–S57  mathnet  crossref  crossref  mathscinet  zmath  isi
    26. A. A. Medovikov, V. I. Lebedev, “Variable time steps optimization of -stable Crank–Nicolson method”, rus j numer anal math mod, 20:3 (2005), 283  crossref  mathscinet  zmath  elib
    27. V. N. Dubinin, S. I. Kalmykov, “A majoration principle for meromorphic functions”, Sb. Math., 198:12 (2007), 1737–1745  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    28. A. L. Lukashov, “Estimates for derivatives of rational functions and the fourth Zolotarev problem”, St. Petersburg Math. J., 19:2 (2008), 253–259  mathnet  crossref  mathscinet  zmath  isi
    29. I. V. Oseledets, “Lower bounds for separable approximations of the Hilbert kernel”, Sb. Math., 198:3 (2007), 425–432  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
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