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Constructive Approximation

, Volume 13, Issue 1, pp 17–27 | Cite as

Exactn-widths of hardy-sobolev classes

  • K. Y. Osipenko
Article

Abstract

Let\(\tilde h^r _{\infty ,\beta } \) and\(\tilde H^r _{\infty ,\beta } \) denote those 2π-periodic, real-valued functions onR that are analytic in the strip |Imz|<β and satisfy the restrictions |Ref (r)(z)| ≤ 1 and |f (r)(z)| ≤ 1, respectively. We determine the Kolmogorov, linear, and Gel’fand widths of\(\tilde h^r _{\infty ,\beta } \) inL q[0, 2π], 1 ≤q ≤ ∞, and\(\tilde H^r _{\infty ,\beta } \) inL [0, 2π].

AMS classification

41A46 30D55 

Key words and phrases

Hardy-Sobolev class n-Width Bounded analytic functions 

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Copyright information

© Springer-Verlag New York Inc 1997

Authors and Affiliations

  • K. Y. Osipenko
    • 1
  1. 1.Department of MathematicsMoscow State University of Aviation TechnologyMoscowRussia

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