Generalized Smoothness Characteristics in Jackson-Type Inequalities and Widths of Classes of Functions in~$L_2$

S. B. Vakarchuk

Matematičeskie zametki, Tome 98 (2015) no. 4, pp. 511-529.

Résumé

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.

Détail

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

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