Entropy numbers and the widths of the classes B_p,θ^r of periodic functionsof many variables - Romanyuk, A. S. (Ukrains’kyi Matematychnyi Zhurnal, 2016)
We establish the exact order estimates for the entropy numbers of the Nikol’skii – Besov classes of periodic functions of two variables in the space L_∞ and use the obtained results in estimating the lower bounds for Kolmogorov, linear, and trigonometric widths. We also study the behavior of similar approximating characteristics of the classes B_p,θ^r of periodic functions of many variables in the spaces L_1 and B_1,1.