On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functions
Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 591-620
Voir la notice de l'article provenant de la source Math-Net.Ru
We solve the problem of the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for the following classes of differentiable periodic functions: $W^r$ ($r>3$), $W^rH_\omega$ (where $\omega$ is a convex modulus of continuity and $r$ is odd), and $W^rL$ ($r=4,6,\dots$).
@article{IM2_1974_8_3_a8,
author = {V. P. Motornyi},
title = {On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functions},
journal = {Izvestiya. Mathematics },
pages = {591--620},
publisher = {mathdoc},
volume = {8},
number = {3},
year = {1974},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a8/}
}
TY - JOUR
AU - V. P. Motornyi
TI - On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functions
JO - Izvestiya. Mathematics
PY - 1974
SP - 591
EP - 620
VL - 8
IS - 3
PB - mathdoc
UR - http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a8/
LA - en
ID - IM2_1974_8_3_a8
ER -
%0 Journal Article
%A V. P. Motornyi
%T On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functions
%J Izvestiya. Mathematics
%D 1974
%P 591-620
%V 8
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a8/
%G en
%F IM2_1974_8_3_a8
V. P. Motornyi. On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functions. Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 591-620. http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a8/