TY - JOUR AU - A. L. Shydlich PY - 2009/10/25 Y2 - 2024/03/29 TI - Order equalities for some functionals and their application to the estimation of the best $n$-term approximations and widths JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 61 IS - 10 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3110 AB - 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. ER -