On average $$$n$$$-widths of certain classes of functions in $$$L_2(\mathbb{R})$$$ space

S.B. Vakarchuk; M.B. Vakarchuk

doi:10.15421/241702

On average $$$n$$$-widths of certain classes of functions in $$$L_2(\mathbb{R})$$$ space

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

Abstract

На классах функций $$$\mathcal{W}^r (\omega_m;\Phi)$$$, где $$$r, m\in \mathbb{N}$$$, $$$\Phi$$$ — мажоранта, $$$\omega_m$$$ — модуль непрерывности m-го порядка, получены оценки сверху и снизу колмогоровского, линейного и бернштейновского средних $$$\nu$$$-поперечников. Также приведено условие, при выполнении которого из указанного результата следуют точные значения перечисленных экстремальных характеристик.

Keywords

average dimension; average $$$\nu$$$-width; majorant; modulus of continuity

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References

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