Geodesic
On the Constant and Step in Jackson's Inequality for Best Approximations by Trigonometric Polynomials and by Haar Polynomials
Matematičeskie zametki, Tome 100 (2016) no. 3, pp. 323-330

Voir la notice de l'article provenant de la source Math-Net.Ru

Two sharp results for best approximations of periodic functions are established in this paper. We prove the sharpness of the step of the modulus of continuity in Jackson's inequality with least possible constant for approximations by trigonometric polynomials. We also prove the sharpness of the constants in a Jackson-type inequality for approximations by Haar polynomials in several variables.
Mots-clés : sharp constant
Keywords: Jackson's inequality, Haar system. 
@article{MZM_2016_100_3_a0,
     author = {P. A. Andrianov and O. L. Vinogradov},
     title = {On the {Constant} and {Step} in {Jackson's} {Inequality} for {Best} {Approximations} by {Trigonometric} {Polynomials} and by {Haar} {Polynomials}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--330},
     publisher = {mathdoc},
     volume = {100},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a0/}
}
TY  - JOUR
AU  - P. A. Andrianov
AU  - O. L. Vinogradov
TI  - On the Constant and Step in Jackson's Inequality for Best Approximations by Trigonometric Polynomials and by Haar Polynomials
JO  - Matematičeskie zametki
PY  - 2016
SP  - 323
EP  - 330
VL  - 100
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a0/
LA  - ru
ID  - MZM_2016_100_3_a0
ER  - 
%0 Journal Article
%A P. A. Andrianov
%A O. L. Vinogradov
%T On the Constant and Step in Jackson's Inequality for Best Approximations by Trigonometric Polynomials and by Haar Polynomials
%J Matematičeskie zametki
%D 2016
%P 323-330
%V 100
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a0/
%G ru
%F MZM_2016_100_3_a0
P. A. Andrianov; O. L. Vinogradov. On the Constant and Step in Jackson's Inequality for Best Approximations by Trigonometric Polynomials and by Haar Polynomials. Matematičeskie zametki, Tome 100 (2016) no. 3, pp. 323-330. http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a0/