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This article is cited in 17 scientific papers (total in 17 papers)
Best Linear Approximation Methods for Functions of Taikov Classes in the Hardy spaces $H_{q,\rho}$, $q\ge1$, $0<\rho\le1$
S. B. Vakarchuka, V. I. Zabutnayab a Ukrainian Academy of Customs
b Dnepropetrovsk National University
Abstract:
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), algebraic polynomial, Minkowski's inequality.
Received: 18.12.2001 Revised: 08.10.2008
Citation:
S. B. Vakarchuk, V. I. Zabutnaya, “Best Linear Approximation Methods for Functions of Taikov Classes in the Hardy spaces $H_{q,\rho}$, $q\ge1$, $0<\rho\le1$”, Mat. Zametki, 85:3 (2009), 323–329; Math. Notes, 85:3 (2009), 322–327
Linking options:
https://www.mathnet.ru/eng/mzm6633https://doi.org/10.4213/mzm6633 https://www.mathnet.ru/eng/mzm/v85/i3/p323
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