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Zap. Nauchn. Sem. POMI, 2009, Volume 366, Pages 67–83 (Mi znsl3482)  

On approximation of functions by trigonometric polynomials with incomplete spectrum in $L_p$, $0<p<1$

Yu. S. Kolomoitsev

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences, Donetsk, Ukraine

Abstract: Suppose $B$ is a subset of integers that possesses certain arithmetic properties. Estimates of the best approximation of functions in the space $L_p$, $0<p<1$, by trigonometric polynomials that are constructed by the system $\{e^{ikx}\}_{k\in\mathbb Z\setminus B}$ are obtained. Bibl. – 13 titles.

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English version:
Journal of Mathematical Sciences (New York), 2010, 165:4, 463–472

UDC: 517.5
Received: 27.11.2008

Citation: Yu. S. Kolomoitsev, “On approximation of functions by trigonometric polynomials with incomplete spectrum in $L_p$, $0<p<1$”, Investigations on linear operators and function theory. Part 37, Zap. Nauchn. Sem. POMI, 366, POMI, St. Petersburg, 2009, 67–83; J. Math. Sci. (N. Y.), 165:4 (2010), 463–472

Citation in format AMSBIB
\Bibitem{Kol09}
\by Yu.~S.~Kolomoitsev
\paper On approximation of functions by trigonometric polynomials with incomplete spectrum in $L_p$, $0<p<1$
\inbook Investigations on linear operators and function theory. Part~37
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 366
\pages 67--83
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3482}
\elib{http://elibrary.ru/item.asp?id=13759399}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 165
\issue 4
\pages 463--472
\crossref{https://doi.org/10.1007/s10958-010-9814-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77949305576}


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