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

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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. Vakarchuk^a, M. Sh. Shabozov^b, M. R. Langarshoev^b

^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}

Linking options:

https://www.mathnet.ru/eng/ivm8909

https://www.mathnet.ru/eng/ivm/y2014/i7/p30

This publication is cited in the following 6 articles:

T. E. Tileubayev, “Exact constants in Jackson–Stechkin inequality in $L^{2}$ with a power-law weight”, Tr. IMM UrO RAN, 29, no. 1, 2023, 259–279
T. E. Tileubaev, “Tochnoe neravenstvo Dzheksona — Stechkina v $L_{2,\mu_{\alpha}}$ ”, Chebyshevskii sb., 24:3 (2023), 139–161
S. B. Vakarchuk, “On Estimates in $L_2(\mathbb{R})$ of Mean $\nu$ -Widths of Classes of Functions Defined via the Generalized Modulus of Continuity of $\omega_{\mathcal{M}}$ ”, Math. Notes, 106:2 (2019), 191–202
S. B. Vakarchuk, “Generalized characteristics of smoothness and some extremal problems in the approximation theory of functions in the space $L_2(\mathbb{R})$ . Ii”, Ukr. Math. J., 70:10 (2019), 1550–1584
S. B. Vakarchuk, “Generalized characteristics of smoothness and some extremal problems in the approximation theory of functions in the space $L_2(\mathbb{R})$ . I”, Ukr. Math. J., 70:9 (2019), 1345–1374
Sergey B. Vakarchuk, “Meansquare Approximation of Function Classes, Given on the all Real Axis R by the Entire Functions of Exponential Type”, IJARM, 6 (2016), 1

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Известия высших учебных заведений. Математика

Russian Mathematics (Izvestiya VUZ. Matematika)

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