Matematičeskie zametki, Tome 62 (1997) no. 2, pp. 192-205
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D. V. Gorbachev. An extremum problem on a class of differentiable functions of several variables. Matematičeskie zametki, Tome 62 (1997) no. 2, pp. 192-205. http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a3/
@article{MZM_1997_62_2_a3,
author = {D. V. Gorbachev},
title = {An extremum problem on a class of differentiable functions of several variables},
journal = {Matemati\v{c}eskie zametki},
pages = {192--205},
year = {1997},
volume = {62},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a3/}
}
TY - JOUR
AU - D. V. Gorbachev
TI - An extremum problem on a class of differentiable functions of several variables
JO - Matematičeskie zametki
PY - 1997
SP - 192
EP - 205
VL - 62
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a3/
LA - ru
ID - MZM_1997_62_2_a3
ER -
%0 Journal Article
%A D. V. Gorbachev
%T An extremum problem on a class of differentiable functions of several variables
%J Matematičeskie zametki
%D 1997
%P 192-205
%V 62
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a3/
%G ru
%F MZM_1997_62_2_a3
On the multidimensional class $W_0^rH_\omega^{(n)}$ of continuous periodic functions $F$ with the $r$th derivative $D^rF$ from $$ H_\omega^{(n)} =\biggl\{f\in C\bigm| |f(x)-f(y)|\le\sum_{i=1}^n\omega_i(|x_i-y_i|) \forall x,y\in\mathbb R^n\biggr\} $$ (where the $\omega_i(x_i)$ are the convex moduli of continuity) and zero mean with respect to each variable, we obtain the exact value of $$ M_r(\omega) =\sup_{F\in W_0^rH_\omega^{(n)}}\|F\|_C. $$
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[2] Korneichuk N. P., Ekstremalnye zadachi teorii priblizhenii, Nauka, M., 1976
[3] Stepanets A. I., “Ob odnoi ekstremalnoi zadache v prostranstve nepreryvnykh funktsii dvukh peremennykh”, Voprosy teorii priblizheniya funktsii i ee prilozhenii, In-t matem. AN USSR, Kiev, 1976, 160–178
[4] Stepanets A. I., Ravnomernye priblizheniya trigonometricheskimi polinomami, Naukova dumka, Kiev, 1981
