@article{Shydlich_2009, title={Order equalities for some functionals and their application to the estimation of the best $n$-term approximations and widths}, volume={61}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/3110}, abstractNote={We study the behavior of functionals of the form $\sup_{l>n} (l-n)\left(∑^l_{k=1} \frac1{ψ^r(k)} \right)^{−1/r}$, where $ψ$ is a positive function, as $n → ∞$: The obtained results are used to establish the exact order equalities (as $n → ∞$) for the best $n$-term approximations of $q$-ellipsoids in metrics of the spaces $S^p_{φ}$: We also consider the applications of the obtained results to the determination of the exact orders of the Kolmogorov widths of octahedra in the Hilbert space.}, number={10}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Shydlich, A. L.}, year={2009}, month={Oct.}, pages={1403-1423} }