Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions - Romanyuk, A.S.; Romanyuk, V.S.; Pozharska, K.V.; Hembars'ka, S.B. (Carpathian Mathematical Publications, 2023)
Exact order estimates for some characteristics of linear and nonlinear approximation of the isotropic Nikol'skii-Besov classes $B^r_{p,θ}$ of periodic multivariate functions in the spaces $B_{q,1}$, $1≤ q ≤ ∞$, are obtained. Among them are the best orthogonal trigonometric approximations, best $m$-term trigonometric approximations, Kolmogorov, linear and trigonometric widths. For all considered characteristics, their estimates coincide in order with the corresponding estimates in the spaces $L_{q}$. Moreover, the obtained exact in order estimates (except the case $1<p<2≤ q < \frac{p}{p-1}$) are realized by the approximation of functions from the classes ${B}^r_{p,θ}$ by trigonometric polynomials with the spectrum in cubic regions. In any case, they do not depend on the smoothness parameter $θ$.