Order equalities for some functionals and their application to the estimation of the best $n$-term approximations and widths

• Date: 2009
• Main Authors: Shydlich, A. L., Шидліч, А. Л.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3110
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 $q$-ellips...