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Mat. Sb. (N.S.), 1972, Volume 87(129), Number 2, Pages 254–274 (Mi msb3048)  

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

Best approximations of functions in the $L_p$ metric by Haar and Walsh polynomials

B. I. Golubov


Abstract: In this work the modulus of continuity of functions in the $L_p$ metric $(1\leqslant p<\nobreak\infty)$ is estimated through its best approximations in this metric by Haar and Walsh polynomials. Besides, estimates of best approximations of functions by Haar and Walsh polynomials in the $L_q$ metric are obtained by the same approximations in the $L_p$ metric $(1\leqslant p<q\leqslant\infty)$. In the last case, the results are analogous to those which were proved for approximations by trigonometric polynomials by P. L. Ul'yanov and also by S. B. Stechkin and A. A. Konyushkov.
Bibliography: 26 titles.

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English version:
Mathematics of the USSR-Sbornik, 1972, 16:2, 265–285

Bibliographic databases:

UDC: 517.5
MSC: Primary 41A30; Secondary 41A10
Received: 11.12.1970

Citation: B. I. Golubov, “Best approximations of functions in the $L_p$ metric by Haar and Walsh polynomials”, Mat. Sb. (N.S.), 87(129):2 (1972), 254–274; Math. USSR-Sb., 16:2 (1972), 265–285

Citation in format AMSBIB
\Bibitem{Gol72}
\by B.~I.~Golubov
\paper Best approximations of functions in the $L_p$ metric by Haar and Walsh polynomials
\jour Mat. Sb. (N.S.)
\yr 1972
\vol 87(129)
\issue 2
\pages 254--274
\mathnet{http://mi.mathnet.ru/msb3048}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=293315}
\zmath{https://zbmath.org/?q=an:0235.42012|0249.42015}
\transl
\jour Math. USSR-Sb.
\yr 1972
\vol 16
\issue 2
\pages 265--285
\crossref{https://doi.org/10.1070/SM1972v016n02ABEH001425}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. È. A. Storozhenko, V. G. Krotov, P. Oswald, “Direct and converse theorems of Jackson type in $L^p$ spaces, $0<p<1$”, Math. USSR-Sb., 27:3 (1975), 355–374  mathnet  crossref  mathscinet  zmath
    2. Oswald P., “Spline Approximation in the Lp-Metric, 0 Less-Than-Or-Equal-to P Less-Than-Or-Equal-to 1”, Math. Nachr., 94 (1980), 69–96  isi
    3. V. I. Ivanov, “Approximation in $L_p$ by polynomials in the Walsh system”, Math. USSR-Sb., 62:2 (1989), 385–402  mathnet  crossref  mathscinet  zmath
    4. G. A. Akishev, “Obobschennaya sistema Khaara i teoremy vlozheniya v simmetrichnye prostranstva”, Fundament. i prikl. matem., 8:2 (2002), 319–334  mathnet  mathscinet  zmath
    5. P. A. Terekhin, “Best approximation of functions in $L_p$ by polynomials on affine system”, Sb. Math., 202:2 (2011), 279–306  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. S. S. Volosivets, “Teoremy vlozheniya dlya $\mathbf{P}$-ichnykh prostranstv Khardi i $VMO$”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4(2) (2014), 518–525  mathnet
    7. S. B. Vakarchuk, A. N. Shchitov, “Estimates for the error of approximation of functions in $L_p^1$ by polynomials and partial sums of series in the Haar and Faber–Schauder systems”, Izv. Math., 79:2 (2015), 257–287  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. S. A. Stasyuk, “Priblizhenie nekotorykh gladkostnykh klassov periodicheskikh funktsii mnogikh peremennykh polinomami po tenzornoi sisteme Khaara”, Tr. IMM UrO RAN, 21, no. 4, 2015, 251–260  mathnet  mathscinet  elib
    9. S. S. Volosivets, B. I. Golubov, “Generalized absolute convergence of series from Fourier coeficients by systems of Haar type”, Russian Math. (Iz. VUZ), 62:1 (2018), 7–16  mathnet  crossref  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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