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Mat. Zametki, 1977, Volume 22, Issue 2, Pages 269–276 (Mi mz8047)  

This article is cited in 3 scientific papers (total in 4 papers)

Absolute values of the coefficients of the polynomials in Weierstrass's approximation theorem

O. A. Muradyan, S. Ya. Khavinson

Moscow Engineering Building Institute

Abstract: The following problem, bound up with Weierstrass's classical approximation theorem, is solved definitively: to determine the sequence of positive numbers $\{M_k\}$ such that, for any $f(z)\in C[0,1]$ and $\forall \varepsilon>0$ there exists the polynomial $P(z)=\sum_0^n\lambda_kz^k$ that $\|f-P\|<\varepsilon$ and $|\lambda_k|<\varepsilon M_k$, $k=1,…,n$.

Full text: PDF file (454 kB)

English version:
Mathematical Notes, 1977, 22:2, 641–645

Bibliographic databases:

UDC: 517.5
Received: 17.11.1975

Citation: O. A. Muradyan, S. Ya. Khavinson, “Absolute values of the coefficients of the polynomials in Weierstrass's approximation theorem”, Mat. Zametki, 22:2 (1977), 269–276; Math. Notes, 22:2 (1977), 641–645

Citation in format AMSBIB
\Bibitem{MurKha77}
\by O.~A.~Muradyan, S.~Ya.~Khavinson
\paper Absolute values of the coefficients of the polynomials in Weierstrass's approximation theorem
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 2
\pages 269--276
\mathnet{http://mi.mathnet.ru/mz8047}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=460974}
\zmath{https://zbmath.org/?q=an:0362.41005}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 2
\pages 641--645
\crossref{https://doi.org/10.1007/BF01780974}


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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. I. F. Krasichkov-Ternovskii, “On absolute completeness of systems of exponentials on a closed interval”, Math. USSR-Sb., 59:2 (1988), 303–315  mathnet  crossref  mathscinet  zmath
    2. A. G. Vitushkin, A. A. Gonchar, M. V. Samokhin, V. M. Tikhomirov, P. L. Ul'yanov, V. P. Havin, V. Ya. Èiderman, “Semën Yakovlevich Khavinson (obituary)”, Russian Math. Surveys, 59:4 (2004), 777–785  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. I. F. Krasichkov-Ternovskii, G. N. Shilova, “Absolute completeness of systems of exponentials on convex compact sets”, Sb. Math., 196:12 (2005), 1801–1814  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. M. A. Petrosova, I. V. Tikhonov, V. B. Sherstyukov, “On growth rate of coefficients in Bernstein polynomials for the standard modulus function on a symmetric interval”, Ufa Math. J., 10:3 (2018), 59–76  mathnet  crossref  isi
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