Geodesic
Sharp Inequalities between the Best Root-Mean-Square Approximations of Analytic Functions in the Disk and Some Smoothness Characteristics in the Bergman Space
Matematičeskie zametki, Tome 110 (2021) no. 2, pp. 266-281

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

In Jackson–Stechkin type inequalities for the smoothness characteristic $\Lambda_m(f)$, $m\in\mathbb N$, we find exact constants determined by averaging the norms of finite differences of $m$th order of a function $f\in B_2$. We solve the problem of best joint approximation for a certain class of functions from $B_2^{(r)}$, $r\in\mathbb Z_+$ whose smoothness characteristic $\Lambda_m(f)$ averaged with a given weight is bounded above by the majorant $\Phi$. The exact values of $n$-widths of some classes of functions are also calculated.
Keywords: sharp inequalities, best joint approximation, smoothness characteristics, $n$-widths.
Mots-clés : exact constants 
@article{MZM_2021_110_2_a8,
     author = {M. Sh. Shabozov and E. U. Kadamshoev},
     title = {Sharp {Inequalities} between the {Best} {Root-Mean-Square} {Approximations} of {Analytic} {Functions} in the {Disk} and {Some} {Smoothness} {Characteristics} in the {Bergman} {Space}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {266--281},
     publisher = {mathdoc},
     volume = {110},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_2_a8/}
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M. Sh. Shabozov; E. U. Kadamshoev. Sharp Inequalities between the Best Root-Mean-Square Approximations of Analytic Functions in the Disk and Some Smoothness Characteristics in the Bergman Space. Matematičeskie zametki, Tome 110 (2021) no. 2, pp. 266-281. http://geodesic.mathdoc.fr/item/MZM_2021_110_2_a8/