The infinite-dimensional widths and optimal recovery of generalized Besov classes

DOI10.1006/JCOM.2002.0639zbMath1020.41015OpenAlexW1980734621MaRDI QIDQ1872635

Yong-ping Liu, Gui Qiao Xu

Publication date: 14 May 2003

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcom.2002.0639

zbMATH Keywords

Besov classesoptimal recoveryinfinite-dimensional width

Mathematics Subject Classification ID

Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (6)

Kolmogorov widths of the classes \(B_{p,\theta}^\Omega\) of periodic functions of many variables in the space \(L_q\) ⋮ Trigonometric widths of classes of periodic functions of many variables ⋮ Approximation of the classes \(B_{p,\theta}^\Omega\) of periodic functions of many variables by Fourier sums in the space \(L_p\) with \(p=1,\infty\) ⋮ \(N\)-widths and average widths of Besov classes in Sobolev spaces ⋮ Characteristics of the linear and nonlinear approximations of the Nikol'skii-Besov-type classes of periodic functions of several variables ⋮ Approximation of functions of many variables from the classes \(B_{p,\theta}^\Omega(\mathbb R^d)\) by entire functions of exponential type

Cites Work

• Infinite-dimensional widths in the spaces of functions. II
• Representation and approximation of periodic functions of several variables with given mixed modulus of continuity
• Some extremal properties of multivariate polynomial splines in the metric \(L_p(\mathbb R^d)\)
• Average widths and optimal recovery of multivariate Besov classes in \(L_p (\mathbb{R}^d)\)
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