Best restricted approximation of smooth function classes

Y. Liu ; G. Xu ; J. Zhang

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 4, pp. 283-294

Résumé

We first discuss the relative Kolmogorov $n$-widths of classes of smooth $2\pi$-periodic functions for which the modulus of continuity of their $r$-th derivatives does not exceed a given modulus of continuity, and then discuss the best restricted approximation of classes of smooth bounded functions defined on the real axis $\mathbb R$ such that the modulus of continuity of their $r$-th derivatives does not exceed a given modulus of continuity by taking the classes of the entire functions of exponential type as approximation tools. Asymptotic results are obtained for these two problems.

Détail

Keywords: modulus of continuity, best restricted approximation, average width.

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