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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2014, Volume 14, Issue 4(1), Pages 407–412 (Mi isu529)  

Mathematics

Some Special Two-dimensional Series of $\{\sin x\sin kx\}$ System and Their Approximation Properties

I. I. Sharapudinov

Daghestan Scientific Centre of Russian Academy of Sciences, 45, Gadgieva str., Makhachkala, Republic of Dagestan, 367000, Russia

Abstract: In present paper there were introduced two-dimensional special series of the system $\{\sin x\sin kx\}$. It's shown that these series have the advantage over two-dimensional cosine Fourier series, because they have better approximation properties near the bounds of the square $[0,1]^2$. It's given convergence speed estimate of special series partial sums to functions $f(x,y)$ from the space of even $2\pi$-periodic continuous functions.

Key words: special series of system $\{\sin x \sin kx\}$, two-dimensional series, piecewise approximation.

DOI: https://doi.org/10.18500/1816-9791-2014-14-4-407-412

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Bibliographic databases:

UDC: 517.538

Citation: I. I. Sharapudinov, “Some Special Two-dimensional Series of $\{\sin x\sin kx\}$ System and Their Approximation Properties”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 14:4(1) (2014), 407–412

Citation in format AMSBIB
\Bibitem{Sha14}
\by I.~I.~Sharapudinov
\paper Some Special Two-dimensional Series of $\{\sin x\sin kx\}$ System and Their Approximation Properties
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2014
\vol 14
\issue 4(1)
\pages 407--412
\mathnet{http://mi.mathnet.ru/isu529}
\crossref{https://doi.org/10.18500/1816-9791-2014-14-4-407-412}
\elib{https://elibrary.ru/item.asp?id=22575449}


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  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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