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Average widths and optimal recovery of multivariate Besov classes in \(L_p (\mathbb{R}^d)\). (English) Zbl 0949.41016

The authors obtain some weak asymptotic results for the average Kolmogorov \(\sigma\)-width and the average linear \(\sigma\)-width of isotropic and anisotropic Besov classes in \(L_p(\mathbb{R}^d)\). For isotropic Besov classes they also investigate the asymptotic behaviour of the optimal recovery.

MSC:

41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
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