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Mat. Zametki, 1976, Volume 19, Issue 1, Pages 49–62 (Mi mz7722)  

This article is cited in 1 scientific paper (total in 1 paper)

Approximation of continuous functions by trigonometric polynomials almost everywhere

T. V. Radoslavova

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: We consider the problem of the rate of approximation of continuous $2\pi$-periodic functions of class $W^rH[\omega]_C$ by trigonometric polynomials of order $n$ on sets of total measure. We prove that when $r\ge0$, $\omega(\delta)\delta^{-1}\to\infty$ ($\delta\to0$) there exists a function $f\in W^rH[\omega]_C$ such that $\widetilde f\in W^rH[\omega]_C$ and for any sequence $\{t_n\}_{n=1}^\infty$ we have almost everywhere on $[0,2\pi]$
\begin{gather*} \varlimsup_{n\to\infty}|f(x)-t_n(x)|n^r\omega^{-1}(1/n)>C_x>0
\varlimsup_{n\to\infty}|\widetilde f(x)-t_n(x)|n^r\omega^{-1}(1/n)>C_x>0 \end{gather*}


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English version:
Mathematical Notes, 1976, 19:1, 29–36

Bibliographic databases:

UDC: 517.5
Received: 24.09.1975

Citation: T. V. Radoslavova, “Approximation of continuous functions by trigonometric polynomials almost everywhere”, Mat. Zametki, 19:1 (1976), 49–62; Math. Notes, 19:1 (1976), 29–36

Citation in format AMSBIB
\Bibitem{Rad76}
\by T.~V.~Radoslavova
\paper Approximation of continuous functions by trigonometric polynomials almost everywhere
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 1
\pages 49--62
\mathnet{http://mi.mathnet.ru/mz7722}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=447939}
\zmath{https://zbmath.org/?q=an:0332.42003|0327.42004}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 1
\pages 29--36
\crossref{https://doi.org/10.1007/BF01147614}


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    This publication is cited in the following articles:
    1. K. I. Oskolkov, “Approximation properties of summable functions on sets of full measure”, Math. USSR-Sb., 32:4 (1977), 489–514  mathnet  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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