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Mat. Sb. (N.S.), 1967, Volume 73(115), Number 4, Pages 630–638 (Mi msb4144)  

This article is cited in 22 scientific papers (total in 23 papers)

On the rapidity of rational approximation of continuous functions with characteristic singularities

A. A. Gončar


Full text: PDF file (753 kB)

English version:
Mathematics of the USSR-Sbornik, 1967, 2:4, 561–568

Bibliographic databases:

Document Type: Article
UDC: 517.512
MSC: 41A20, 26C15
Received: 30.03.1967

Citation: A. A. Gončar, “On the rapidity of rational approximation of continuous functions with characteristic singularities”, Mat. Sb. (N.S.), 73(115):4 (1967), 630–638; Math. USSR-Sb., 2:4 (1967), 561–568

Citation in format AMSBIB
\Bibitem{Gon67}
\by A.~A.~Gon{\v{c}}ar
\paper On the rapidity of rational approximation of continuous functions with characteristic singularities
\jour Mat. Sb. (N.S.)
\yr 1967
\vol 73(115)
\issue 4
\pages 630--638
\mathnet{http://mi.mathnet.ru/msb4144}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=214982}
\zmath{https://zbmath.org/?q=an:0175.06001}
\transl
\jour Math. USSR-Sb.
\yr 1967
\vol 2
\issue 4
\pages 561--568
\crossref{https://doi.org/10.1070/SM1967v002n04ABEH002355}


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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, “On the order of approximation of convex functions by rational functions”, Math. USSR-Izv., 3:5 (1969), 1067–1080  mathnet  crossref  mathscinet  zmath
    2. A. P. Bulanov, “Rational approximations to convex functions with given modulus of continuity”, Math. USSR-Sb., 13:3 (1971), 473–490  mathnet  crossref  mathscinet  zmath
    3. K. N. Lungu, “On best approximations by rational functions with a fixed number of poles”, Math. USSR-Sb., 15:2 (1971), 313–324  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. V. A. Popov, P. P. Petrushev, “The exact order of the best approximation to convex functions by rational functions”, Math. USSR-Sb., 32:2 (1977), 245–251  mathnet  crossref  mathscinet  zmath  isi
    6. A.R Reddy, “Recent advances in Chebyshev rational approximation on finite and infinite intervals”, Journal of Approximation Theory, 22:1 (1978), 59  crossref
    7. P. P. Petrushev, “Uniform rational approximations of functions of class $V_r$”, Math. USSR-Sb., 36:3 (1980), 389–403  mathnet  crossref  mathscinet  zmath  isi
    8. 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
    9. Frank Stenger, “Numerical Methods Based on Whittaker Cardinal, or Sinc Functions”, SIAM Rev, 23:2 (1981), 165  crossref  mathscinet  zmath  isi
    10. Petrushev P., “Relations Between Rational and Spline Approximations”, Acta Math. Hung., 44:1-2 (1984), 61–83  crossref  isi
    11. V. N. Rusak, “Sharp order estimates for best rational approximations in classes of functions representable as convolutions”, Math. USSR-Sb., 56:2 (1987), 491–513  mathnet  crossref  mathscinet  zmath
    12. 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
    13. Charles K Chui, Xian-Liang Shi, “Characterization of weights in best rational weighted approximation of piecewise smooth functions, I”, Journal of Approximation Theory, 54:2 (1988), 180  crossref
    14. 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
    15. Stahl H., “Best Uniform Rational Approximation of X-Alpha on [0, 1]”, Bull. Amer. Math. Soc., 28:1 (1993), 116–122  crossref  isi
    16. 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
    17. Rovba YA., “Approximation of Functions Differentiated According to Riemann-Liuvill by Rational Operators”, Dokl. Akad. Nauk Belarusi, 40:6 (1996), 18–22  isi
    18. A. K. Ramazanov, “Rational approximation with sign-sensitive weight”, Math. Notes, 60:5 (1996), 536–543  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. 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
    20. 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
    21. A. P. Starovoitov, “Rational Approximations of Riemann–Liouville and Weyl Fractional Integrals”, Math. Notes, 78:3 (2005), 391–402  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    22. Yu. A. Labych, A. P. Starovoitov, “Priblizhenie nepreryvnykh funktsii ratsionalnymi drobyami Pade–Chebysheva”, PFMT, 2011, no. 1(6), 69–78  mathnet
    23. 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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