Matematičeskie zametki, Tome 17 (1975) no. 4, pp. 531-543
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V. P. Motornyi; V. I. Ruban. Diameters of some classes of differentiable periodic functions in the space $L$. Matematičeskie zametki, Tome 17 (1975) no. 4, pp. 531-543. http://geodesic.mathdoc.fr/item/MZM_1975_17_4_a4/
@article{MZM_1975_17_4_a4,
author = {V. P. Motornyi and V. I. Ruban},
title = {Diameters of some classes of differentiable periodic functions in the space $L$},
journal = {Matemati\v{c}eskie zametki},
pages = {531--543},
year = {1975},
volume = {17},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_4_a4/}
}
TY - JOUR
AU - V. P. Motornyi
AU - V. I. Ruban
TI - Diameters of some classes of differentiable periodic functions in the space $L$
JO - Matematičeskie zametki
PY - 1975
SP - 531
EP - 543
VL - 17
IS - 4
UR - http://geodesic.mathdoc.fr/item/MZM_1975_17_4_a4/
LA - ru
ID - MZM_1975_17_4_a4
ER -
%0 Journal Article
%A V. P. Motornyi
%A V. I. Ruban
%T Diameters of some classes of differentiable periodic functions in the space $L$
%J Matematičeskie zametki
%D 1975
%P 531-543
%V 17
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1975_17_4_a4/
%G ru
%F MZM_1975_17_4_a4
In this paper, diameters in the sense of A. N. Kolmogorov are found for the class of $2\pi$-periodic functions $W^{(r)}H_\omega$ in the space $L$, that is, $d_{2n-1}(W^{(r)}H_\omega, L)$, where $\omega(t)$ is an upper-convex regular modulus of continuity ($r,n=1,2,\dots$). An estimate from below is found for diameters in the sense of I. M. Gel'fand, that is, $d^{2n-1}(W^{(r)}H_\omega, L)$
