Order equalities for some functionals and their application to the estimation of the best n-term approximations and widths - Shydlich, A. L. (Ukrains’kyi Matematychnyi Zhurnal, 2009)
We study the behavior of functionals of the form _l>n (l-n)(∑^l_k=1 1ψ^r(k) )^−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.