Estimates for certain approximation characteristics of Nikol'skii-Besov spaces with generalized mixed smoothness (Q735998)

The author presents (without proofs) sharp estimates for approximations by Fourier sums, for the best \(N\)-term trigonometric approximations, and for the trigonometric and Kolmogorov widths of the unit ball in the Nikolskii-Besov space \(MB^{s,\varepsilon}_{p\theta} (\mathbb T^d)\) of generalized mixed smoothness (\(s\in (0,\infty)^n\), \(1<p<\infty\), \(1\leq\theta\leq\infty\), \(1\leq n \leq d\)) in the metric of the space \(L_q (\mathbb T^d)\) \((1<q<\infty)\). Aperiodic analogues of the first three characteristics are also considered.