Estimates for the widths of classes of periodic functions of several variables. I. (English) Zbl 1216.41021

Bazarkhanov, D. B.

Eurasian Math. J. 1, No. 3, 11-26 (2010).

Summary: We establish estimates sharp in order for the Kolmogorov and linear widths of the classes \(B_{pq}^{sm}(\mathbb T^k)\) and \(L_{pq}^{sm}(\mathbb T^k)\) of Nikol’skii-Besov, Lizorkin-Triebel types, respectively, in the space \(L_r(\mathbb T^k)\) for a certain range of the parameters \(s,p,q,r\), and \(m\).

MSC:

41A46	Approximation by arbitrary nonlinear expressions; widths and entropy
41A63	Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
42C40	Nontrigonometric harmonic analysis involving wavelets and other special systems

Keywords:

Kolmogorov width; linear width; function class; mixed smoothness; wavelet