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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, Number 7, Pages 30–48 (Mi ivm8909)  
This article is cited in 6 scientific papers (total in 6 papers)

On the best mean square approximations by entire functions of exponential type in $L_2(\mathbb R)$ and mean $\nu$-widths of some functional classes

S. B. Vakarchuka, M. Sh. Shabozovb, M. R. Langarshoevb

a Chair of Information Science and Mathematical Methods in Economics, Alfred Nobel University, 18 Naberezhnaya Lenina str., Dnepropetrovsk, 49000 Ukraine
b Institute of Mathematics, Academy of Sciences, Republic Tajikistan, 299/1 Aini str., Dushanbe, 734063 Republic of Tajikistan
Full-text PDF (273 kB) Citations (6)
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Abstract: We consider some extremal problems of approximation theory of functions at the whole real axis $\mathbb R$ by entire functions of the exponential type. In particular, we find the exact values of the mean $\nu$-widths of classes of functions, defined by the moduli of continuity of $m$th order $\omega_m$ and majorants $\Psi$ satisfying the special type of restriction.
Keywords: best approximation, entire function of exponential type, modulus of continuity, mean $\nu$-width, majorant.
Received: 18.01.2013
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2014, Volume 58, Issue 7, Pages 25–41
DOI: https://doi.org/10.3103/S1066369X14070032
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: S. B. Vakarchuk, M. Sh. Shabozov, M. R. Langarshoev, “On the best mean square approximations by entire functions of exponential type in $L_2(\mathbb R)$ and mean $\nu$-widths of some functional classes”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 7, 30–48; Russian Math. (Iz. VUZ), 58:7 (2014), 25–41
Citation in format AMSBIB
\Bibitem{VakShaLan14}
\by S.~B.~Vakarchuk, M.~Sh.~Shabozov, M.~R.~Langarshoev
\paper On the best mean square approximations by entire functions of exponential type in $L_2(\mathbb R)$ and mean $\nu$-widths of some functional classes
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2014
\issue 7
\pages 30--48
\mathnet{http://mi.mathnet.ru/ivm8909}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2014
\vol 58
\issue 7
\pages 25--41
\crossref{https://doi.org/10.3103/S1066369X14070032}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84903692287}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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