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Mat. Sb. (N.S.), 1975, Volume 96(138), Number 2, Pages 171–188 (Mi msb3122)  

This article is cited in 9 scientific papers (total in 9 papers)

Asymptotic behavior of the least deviations of the function $\operatorname{sgn}x$ from rational functions

A. P. Bulanov


Abstract: It is shown that the best uniform approximation of $\operatorname{sgn}x$ by rational functions of order at most $n$ on the union of the two intervals $[-1,-\delta]\cup[\delta,1]$ ($0<\delta<1$) does not exceed
$$ e^{\frac{\pi^2}2}\exp\{-\frac{\pi^2}2\frac n{\ln\frac1\delta+2\ln\ln\frac e\delta+2}\}. $$

Bibliography: 10 titles.

Full text: PDF file (1191 kB)
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English version:
Mathematics of the USSR-Sbornik, 1975, 25:2, 159–176

Bibliographic databases:

UDC: 517.5
MSC: 41A20, 41A50
Received: 25.12.1973

Citation: A. P. Bulanov, “Asymptotic behavior of the least deviations of the function $\operatorname{sgn}x$ from rational functions”, Mat. Sb. (N.S.), 96(138):2 (1975), 171–188; Math. USSR-Sb., 25:2 (1975), 159–176

Citation in format AMSBIB
\Bibitem{Bul75}
\by A.~P.~Bulanov
\paper Asymptotic behavior of the least deviations of the function $\operatorname{sgn}x$ from rational functions
\jour Mat. Sb. (N.S.)
\yr 1975
\vol 96(138)
\issue 2
\pages 171--188
\mathnet{http://mi.mathnet.ru/msb3122}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=370006}
\zmath{https://zbmath.org/?q=an:0317.41012}
\transl
\jour Math. USSR-Sb.
\yr 1975
\vol 25
\issue 2
\pages 159--176
\crossref{https://doi.org/10.1070/SM1975v025n02ABEH002204}


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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. P. Bulanov, “Rational approximation of continuous functions of finite variation”, Math. USSR-Izv., 9:5 (1975), 1081–1118  mathnet  crossref  mathscinet  zmath
    2. E. P. Dolzhenko, V. I. Danchenko, “Dependence of the differentiability of functions of several variables on their rate of approximation by rational functions”, Math. USSR-Izv., 11:1 (1977), 171–192  mathnet  crossref  mathscinet  zmath
    3. 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
    4. A.R Reddy, “Recent advances in Chebyshev rational approximation on finite and infinite intervals”, Journal of Approximation Theory, 22:1 (1978), 59  crossref
    5. Vladov N., “Exact Asymptotics for the Rational Approximation of Sign(X) in Hausdorff Metric”, 39, no. 7, 1986, 37–40  mathscinet  zmath  isi
    6. A.-R. K. Ramazanov, “Rational approximation of functions with finite variation in the Orlicz metric”, Math. Notes, 54:2 (1993), 811–820  mathnet  crossref  mathscinet  zmath  isi
    7. A. P. Bulanov, “Rational approximation of functions of several variables with finite Hardy variation”, Sb. Math., 186:11 (1995), 1599–1620  mathnet  crossref  mathscinet  zmath  isi
    8. V. I. Danchenko, “Estimates of derivatives of simplest fractions and other questions”, Sb. Math., 197:4 (2006), 505–524  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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