On generalized characteristics of smoothness of functions and on average $$$\nu$$$-widths in the space $$$L_2(\mathbb{R})$$$

S.B. Vakarchuk; M.B. Vakarchuk

doi:10.15421/241902

On generalized characteristics of smoothness of functions and on average $$$\nu$$$-widths in the space $$$L_2(\mathbb{R})$$$

S.B. Vakarchuk (Alfred Nobel University), https://orcid.org/0000-0002-2562-8844
M.B. Vakarchuk (Oles Honchar Dnipro National University), https://orcid.org/0000-0001-8606-9057

Abstract

Estimates above and estimates below have been obtained for Kolmogorov, linear and Bernshtein average $$$\nu$$$-widths on the classes of functions $$$W^r (\omega^w, \Psi)$$$, where $$$r \in \mathbb{N}$$$, $$$\omega^w(f)$$$ is the generalized characteristic of smoothness of a function $$$f \in L_2(\mathbb{R})$$$, $$$\Psi$$$ is a majorant. Exact values of the enumerated extremal characteristics of approximation, following from the one condition on the majorant were obtained too.

Keywords

generalized modulus of continuity; majorant; entire function; average $$$\nu$$$-width; Fourier transform

MSC 2020

41A35; 41A44; 42A38; 30D20

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References

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