Geodesic
Generalized Smoothness Characteristics in Jackson-Type Inequalities and Widths of Classes of Functions in~$L_2$
Matematičeskie zametki, Tome 98 (2015) no. 4, pp. 511-529

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In the space $L_2$, we study a number of smoothness characteristics of functions; our study is based on the use of the generalized shift operator $\tau_h$. For the case in which $\tau$ is the Steklov operator $S$, we obtain exact constants in Jackson-type inequalities for some classes of $2\pi$-periodic functions. We also calculate the exact values of the $n$-widths of function classes defined by the smoothness characteristics under consideration.
Keywords: Jackson-type inequality, $n$-width of a function class, Steklov operator, smoothness characteristic, generalized shift operator $\tau_h$, Minkowski's inequality, trigonometric polynomial, Rolle's theorem.
Mots-clés : majorant 
@article{MZM_2015_98_4_a2,
     author = {S. B. Vakarchuk},
     title = {Generalized {Smoothness} {Characteristics} in {Jackson-Type} {Inequalities} and {Widths} of {Classes} of {Functions} in~$L_2$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {511--529},
     publisher = {mathdoc},
     volume = {98},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_4_a2/}
}
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S. B. Vakarchuk. Generalized Smoothness Characteristics in Jackson-Type Inequalities and Widths of Classes of Functions in~$L_2$. Matematičeskie zametki, Tome 98 (2015) no. 4, pp. 511-529. http://geodesic.mathdoc.fr/item/MZM_2015_98_4_a2/