Affiliation:
1. Lesya Ukrainka Volyn National University, Lutsk, Ukraine
Abstract
Estimates that are accurate by order of magnitude have been obtained for
some characteristics of the linear and nonlinear approximations of the
isotropic classes of the Nikol'skii--Besov-type \textit{$\mathbf{B}%
^{\,\omega}_{p,\theta}$} of periodic functions of several variables in the
spaces $B_{q,1}, 1 \leq q \leq \infty$. A specific feature of those spaces,
as linear subspaces of $L_q$, is that the norm in them is ``stronger'' than
the $L_q$-norm.
Publisher
Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine
Reference46 articles.
1. Temlyakov, V. N. (1989). Estimates of the asymptotic characteristics of classes of functions with bounded mixed derivative or difference. Tr. Mat. Inst. Steklova, 189, 138–168.
2. Kashin, B. S. & Temlyakov, V. N. (1994). On the best m-term approximations and entropy of sets in the space L1. Mat. notes, 56(5), 57–86.
3. Belinsky, E. S. (1998). Estimates of entropy numbers and Gaussian measures for classes of functions with bounded mixed derivative. J. Approxim. Theory, 93, 114–127. https://doi.org/10.1006/jath.1997.3157
4. Romanyuk, A. S. (2016). Entropy numbers and widths of the classes Br p,θ of periodic functions of several variables. Ukr. Mat. Zhurn., 68(10), 1403–1417.
5. Romanyuk, A. S. & Romanyuk, V. S. (2019). Approximation characteristics of the classes of periodic functions of several variables in the space B∞,1. Ukr. Mat. Zhurn., 71(2), 271–278. https://doi.org/10.1007/bf01056698