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 Mat. Zametki: Year: Volume: Issue: Page: Find

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

Approximation of continuous functions by trigonometric polynomials almost everywhere

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

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
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