The best M-term trigonometric approximations of the classes of periodic multivariate functions with bounded generalized derivative in the space Lq
- Authors: Shvai K.V.1
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Affiliations:
- Institute of Mathematics of the NAS of Ukraine
- Issue: Vol 222, No 6 (2017)
- Pages: 750-761
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/239265
- DOI: https://doi.org/10.1007/s10958-017-3329-0
- ID: 239265
Cite item
Abstract
The order estimates of the best M-term trigonometric approximations of functions \( {D}_{\beta}^{\psi } \) and the classes of (ψ , β)-differentiable periodic multivariate functions in the space Lq, 2 ≤ q < ∞ are obtained. It is shown that, under certain conditions imposed on the parameter q; the best M-term trigonometric approximations \( {e}_M{\left({L}_{\beta, 1}^{\psi}\right)}_q \) have better order than the best orthogonal trigonometric approximations \( e\frac{1}{M}{\left({L}_{\beta, 1}^{\psi}\right)}_q \).
About the authors
Kateryna V. Shvai
Institute of Mathematics of the NAS of Ukraine
Author for correspondence.
Email: kate.shvai@gmail.com
Ukraine, Kiev