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Mat. Sb. (N.S.), 1982, Volume 117(159), Number 1, Pages 114–130 (Mi msb2185)  

This article is cited in 10 scientific papers (total in 10 papers)

Rational approximations of absolutely continuous functions with derivative in an Orlicz space

A. A. Pekarskii


Abstract: Let $R_n(f)$ be the best uniform approximation of $f \in C[0,1]$ by rational fractions of degree at most $n$, and let $ W[0,1]$ be the set of monotone convex functions $w\in C[0,1]$ such that $w(0)=0$ and $w(1)=1$.
Theorem 1. Suppose the function $f$ is absolutely continuous on the interval $[0,1],$ and let $w\in W[0,1]$ and $\widehat f= f(w(x))$. If $|\widehat f'|\ln^+|\widehat f'|$ is summable on $[0,1],$ then $R_n(f)=o(1/n)$.
Various applications and generalizations of this result are given, and the periodic case is also considered.
Bibliography: 23 titles.

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English version:
Mathematics of the USSR-Sbornik, 1983, 45:1, 121–137

Bibliographic databases:

UDC: 517.5
MSC: Primary 26A46, 41A20, 46E30; Secondary 41A50
Received: 28.03.1980

Citation: A. A. Pekarskii, “Rational approximations of absolutely continuous functions with derivative in an Orlicz space”, Mat. Sb. (N.S.), 117(159):1 (1982), 114–130; Math. USSR-Sb., 45:1 (1983), 121–137

Citation in format AMSBIB
\Bibitem{Pek82}
\by A.~A.~Pekarskii
\paper Rational approximations of absolutely continuous functions with derivative in an Orlicz space
\jour Mat. Sb. (N.S.)
\yr 1982
\vol 117(159)
\issue 1
\pages 114--130
\mathnet{http://mi.mathnet.ru/msb2185}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=642493}
\zmath{https://zbmath.org/?q=an:0525.41015}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 45
\issue 1
\pages 121--137
\crossref{https://doi.org/10.1070/SM1983v045n01ABEH002590}


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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. Starovoitov A., “Rational Approximation of Functions with a Derivative with a Finite Variation”, Dokl. Akad. Nauk Belarusi, 28:2 (1984), 104–106  mathscinet  isi
    2. Devore R., “Approximation by Rational Functions”, Proc. Amer. Math. Soc., 98:4 (1986), 601–604  crossref  mathscinet  zmath  isi
    3. 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
    4. Pekarskii A., “Direct and Inverse-Theorems of the Rational Approximation and Differential Properties of the Functions”, Dokl. Akad. Nauk Belarusi, 31:6 (1987), 500–503  mathscinet  isi
    5. Pekarskii A., “Direct and Converse Theorems of Rational Approximation in the Spaces Lp[-1,1] and C[-1,1]”, 293, no. 6, 1987, 1307–1310  mathscinet  isi
    6. Moskona E., Petrushev P., “Characterization of the Rational Approximation in Uniform Metrics”, 42, no. 2, 1989, 37–40  mathscinet  zmath  isi
    7. Moskona E., Petrushey P., “Uniform Rational Approximation of Functions with 1st Derivative in the Real Hardy Space Re H1”, Constr. Approx., 7:1 (1991), 69–103  crossref  mathscinet  zmath  isi
    8. A. A. Pekarskii, “Uniform rational approximations and Hardy–Sobolev spaces”, Math. Notes, 56:4 (1994), 1082–1088  mathnet  crossref  mathscinet  zmath  isi
    9. V. N. Rusak, I. V. Rybachenko, “The Properties of Functions and Approximation by Summation Rational Operators on the Real Axis”, Math. Notes, 76:1 (2004), 103–110  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. Jafarov S.Z., “Approximation of Conjugate Functions by Trigonometric Polynomials in Weighted Orlicz Spaces”, J. Math. Inequal., 7:2 (2013), 271–281  crossref  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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