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

  • A. L. Shydlich


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.
How to Cite
Shydlich, A. L. “Order Equalities for Some Functionals and Their Application to the Estimation of the Best $n$-Term Approximations and Widths”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, no. 10, Oct. 2009, pp. 1403-2, https://umj.imath.kiev.ua/index.php/umj/article/view/3110.
Research articles