Geodesic
On Estimates in~$L_2(\mathbb{R})$ of Mean $\nu$-Widths of Classes of Functions Defined via the Generalized Modulus of Continuity of~$\omega_{\mathcal{M}}$
Matematičeskie zametki, Tome 106 (2019) no. 2, pp. 198-211

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For the classes of functions $$ W^r(\omega_{\mathcal{M}},\Phi):=\{f \in L^r_2(\mathbb{R}): \omega_{\mathcal{M}}(f^{(r)},t) \le \Phi(t) \ \forall\,t \in (0,\infty)\}, $$ where $\Phi$ is a majorant and $r \in \mathbb{Z}_{+}$, lower and upper bounds for the Bernstein, Kolmogorov, and linear mean $\nu$-widths in the space $L_2(\mathbb{R})$ are obtained. A condition on the majorant $\Phi$ under which the exact values of these widths can be calculated is indicated. Several examples illustrating the results are given.
Keywords: mean dimension, mean $\nu$-width, entire function of exponential type, generalized modulus of continuity.
Mots-clés : majorant 
@article{MZM_2019_106_2_a3,
     author = {S. B. Vakarchuk},
     title = {On {Estimates} in~$L_2(\mathbb{R})$ of {Mean} $\nu${-Widths} of {Classes} of {Functions} {Defined} via the {Generalized} {Modulus} of {Continuity} of~$\omega_{\mathcal{M}}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {198--211},
     publisher = {mathdoc},
     volume = {106},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_2_a3/}
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S. B. Vakarchuk. On Estimates in~$L_2(\mathbb{R})$ of Mean $\nu$-Widths of Classes of Functions Defined via the Generalized Modulus of Continuity of~$\omega_{\mathcal{M}}$. Matematičeskie zametki, Tome 106 (2019) no. 2, pp. 198-211. http://geodesic.mathdoc.fr/item/MZM_2019_106_2_a3/