V. I. Ruban, “Even diameters of the classes $W^{(r)}H_\omega$ in the space $C_2\pi$”, Mat. Zametki, 15:3 (1974), 387–392; Math. Notes, 15:3 (1974), 222

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Matematicheskie Zametki, 1974, Volume 15, Issue 3, Pages 387–392 (Mi mzm7359)

This article is cited in 4 scientific papers (total in 4 papers)

Even diameters of the classes

W^{(r)} H_{ω}

$W^{(r)}H_\omega$ in the space

C_{2} π

$C_2\pi$

V. I. Ruban

Dnepropetrovsk State University

Full-text PDF (360 kB) Citations (4)

Abstract: For even values of

n

$n$ we find the exact values of the diameters

d_{n} (W^{(r)} H_{ω})

$d_n(W^{(r)}H_\omega)$ of the classes of

2 π

$2\pi$ -periodic functions

W^{(r)} H_{ω}

$W^{(r)}H_\omega$ (

ω (t)

$\omega(t)$ is an arbitrary convex upwards modulus of continuity) in the space

C_{2} π

$C_2\pi$ . We find that

d_{2 n} (W^{(r)} H_{ω})

$d_{2n}(W^{(r)}H_\omega)$ (

n = 1, 2, \dots

$n=1,2,\dots$ ;

r = 0, 1, 2, \dots

$r=0,1,2,\dots$ ).

Received: 29.05.1973

English version:
Mathematical Notes, 1974, Volume 15, Issue 3, Pages 222–225
DOI: https://doi.org/10.1007/BF01438374

Bibliographic databases:

UDC: 517.5

Language: Russian

Citation: V. I. Ruban, “Even diameters of the classes

W^{(r)} H_{ω}

$W^{(r)}H_\omega$ in the space

C_{2} π

$C_2\pi$ ”, Mat. Zametki, 15:3 (1974), 387–392; Math. Notes, 15:3 (1974), 222–225

Citation in format AMSBIB

\Bibitem{Rub74}

\by V.~I.~Ruban

\paper Even diameters of the classes $W^{(r)}H_\omega$ in the space $C_2\pi$

\jour Mat. Zametki

\yr 1974

\vol 15

\issue 3

\pages 387--392

\mathnet{http://mi.mathnet.ru/mzm7359}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=352814}

\zmath{https://zbmath.org/?q=an:0297.41023}

\transl

\jour Math. Notes

\yr 1974

\vol 15

\issue 3

\pages 222--225

\crossref{https://doi.org/10.1007/BF01438374}

Linking options:

https://www.mathnet.ru/eng/mzm7359

https://www.mathnet.ru/eng/mzm/v15/i3/p387

This publication is cited in the following 4 articles:

S. K. Bagdasarov, “Maximization of functionals in $H^\omega [a,b]$ ”, Sb. Math., 189:2 (1998), 159–226
V. T. Shevaldin, “Lower estimates of the widths of the classes of functions defined by a modulus of continuity”, Russian Acad. Sci. Izv. Math., 45:2 (1995), 399–415
N. P. Korneichuk, “Widths in $L_p$ of classes of continuous and of differentiable functions, and optimal methods of coding and recovering functions and their derivatives”, Math. USSR-Izv., 18:2 (1982), 227–247
N. P. Korneichuk, “On extremal problems in the theory of best approximation”, Russian Math. Surveys, 29:3 (1974), 7–43

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

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