Best Linear Approximation Methods for Functions of Taikov Classes in the Hardy spaces $H_{q,\rho}$, $q\ge1$, $0<\rho\le1$

S. B. Vakarchuk; V. I. Zabutnaya

Geodesic

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Best Linear Approximation Methods for Functions of Taikov Classes in the Hardy spaces $H_{q,\rho}$, $q\ge1$, $0\rho\le1$

S. B. Vakarchuk ; V. I. Zabutnaya

Matematičeskie zametki, Tome 85 (2009) no. 3, pp. 323-329

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Résumé

In the Hardy spaces $H_{q,\rho}$, $q\ge1$, $0\rho\le1$, we construct best linear approximation methods for classes of analytic functions $W^rH_q\Phi$, $r\in\mathbb N$, in the unit disk (studied by L. V. Taikov) whose averaged second-order moduli of continuity of the angular boundary values of the $r$th derivatives are majorized by a given function $\Phi$ satisfying certain constraints.

Keywords: linear approximation of functions, analytic function, Hardy spaces $H_{q,\rho}$, modulus of continuity, $n$-width (Bernstein, Kolmogorov, Gelfand), Minkowski's inequality.
Mots-clés : algebraic polynomial

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     author = {S. B. Vakarchuk and V. I. Zabutnaya},
     title = {Best {Linear} {Approximation} {Methods} for {Functions} of {Taikov} {Classes} in the {Hardy} spaces $H_{q,\rho}$, $q\ge1$, $0<\rho\le1$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--329},
     publisher = {mathdoc},
     volume = {85},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_3_a0/}
}

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S. B. Vakarchuk; V. I. Zabutnaya. Best Linear Approximation Methods for Functions of Taikov Classes in the Hardy spaces $H_{q,\rho}$, $q\ge1$, $0<\rho\le1$. Matematičeskie zametki, Tome 85 (2009) no. 3, pp. 323-329. http://geodesic.mathdoc.fr/item/MZM_2009_85_3_a0/