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Ukrainian Mathematical Journal

, Volume 61, Issue 10, pp 1649–1671 | Cite as

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

  • A. L. Shydlich
Article
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We study the behavior of functionals of the form
$$ \mathop {\sup }\limits_{l > n} \left( {l - n} \right){\left( {\sum\limits_{k = 1}^l {\frac{1}{{{\psi^r}(k)}}} } \right)^{{{ - 1} \mathord{\left/{\vphantom {{ - 1} r}} \right.} r}}}, $$
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.

Keywords

Hilbert Space Natural Number Approximation Theory Extremal Problem Order Equality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • A. L. Shydlich
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine

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