We study the behavior of functionals of the form
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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 10, pp. 1403–1423, October, 2009.
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Shydlich, A.L. Order equalities for some functionals and their application to the estimation of the best n-term approximations and widths. Ukr Math J 61, 1649–1671 (2009). https://doi.org/10.1007/s11253-010-0304-z
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DOI: https://doi.org/10.1007/s11253-010-0304-z