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Trudy Inst. Mat. i Mekh. UrO RAN, 2018, Volume 24, Number 4, Pages 217–224 (Mi timm1588)  

Analysis of a theorem on the Jackson-Stechkin inequality in the Bergman space $B_2$

M. S. Saidusajnov

University of Central Asia

Abstract: We present a refinement of a theorem of V.A. Abilov, F.V. Abilova, and M.K. Kerimov on the exact constant in a Jackson type inequality between the mean-square approximation of a function of a complex variable by Fourier series in a system orthogonal in a bounded domain and the generalized modulus of continuity of order $m\geq 1$.

Keywords: generalized modulus of continuity, generalized translation operator, orthonormal system, Jackson-Stechkin inequality.

DOI: https://doi.org/10.21538/0134-4889-2018-24-4-217-224

Full text: PDF file (185 kB)
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Bibliographic databases:

UDC: 517.5
MSC: 42C10, 47A58
Received: 28.06.2018
Revised: 15.11.2018
Accepted:19.11.2018

Citation: M. S. Saidusajnov, “Analysis of a theorem on the Jackson-Stechkin inequality in the Bergman space $B_2$”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 4, 2018, 217–224

Citation in format AMSBIB
\Bibitem{Sai18}
\by M.~S.~Saidusajnov
\paper Analysis of a theorem on the Jackson-Stechkin inequality in the Bergman space $B_2$
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2018
\vol 24
\issue 4
\pages 217--224
\mathnet{http://mi.mathnet.ru/timm1588}
\crossref{https://doi.org/10.21538/0134-4889-2018-24-4-217-224}
\elib{http://elibrary.ru/item.asp?id=36517712}


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