Best bilinear approximations of the classes \(S_{p,\theta}^\Omega B\) of periodic functions of many variables
type: Item
instance of: scholarly article
title: Best bilinear approximations of the classes \(S_{p,\theta}^\Omega B\) of periodic functions of many variables
zbMATH Open document ID: 1259.41041
published in: Ukrainian Mathematical Journal
publication date: 2012-11-23T00:00:00Z
review text: The author obtains exact order-estimates for the best bilinear approximation of certain subsets \(S^{\Omega}_{p,\theta}B\) of periodic functions of several variables in the space \(L_q([-\pi,\pi])^d\), under certain restrictions on the parameters \(p\), \(q\) and \(\theta\). For \(1 \leq p <\infty\), the definition of the spaces \(S^{\Omega}_{p,\theta}B\) used by the author is taken (with a slight modification) from [\textit{Y. Sun} and \textit{H. Wang}, Proc. Steklov Inst. Math. 219, 350--371 (1997) and Tr. Mat. Inst. Steklova 219, 356--377 (1997; Zbl 1032.42015)]. For \(p=\infty\), the definition coincides with that of \(S^{\Omega}_{p} H\) in [\textit{N. N. Pustovojtov}, Anal. Math. 20, No. 1, 35--48 (1994; Zbl 0791.42014)].
reviewed by: Richard A. Zalik
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 6110014
zbMATH Keywords: almost increasing and almost decreasing functions
zbMATH Keywords: Bari-Stechkin condition
zbMATH Keywords: Nilol'skii-Besov spaces
zbMATH Keywords: modulus of continuity
zbMATH Keywords: de la Valleé Poussin kernel
zbMATH Keywords: trigonometric approximation
zbMATH Keywords: bilinear approximation
zbMATH Keywords: Kolmogorov width
zbMATH Keywords: Rudin-Shapiro polynomials
author: K. V. Solich
MaRDI profile type: Publication
full work available at URL: s11253-011-0554-4
OpenAlex ID: W1988961654
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cites work: Best Approximations and Kolmogorov and Trigonometric Widths of the Classes B Ω p,θ of Periodic Functions of Many Variables
DOI: 10.1007/S11253-011-0554-4
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description: scientific article; zbMATH DE number 6110014