Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (4): 1001-1011.

• Articles • Previous Articles     Next Articles

Infinite-dimensional Widths and Optimal Recovery of Besov-Wiener Classes of Multivariate Functions

  

  1. (College of Mathematical Science, Tianjin Normal University, Tianjin 300387)
  • Received:2007-02-26 Revised:2008-03-08 Online:2009-08-25 Published:2009-08-25
  • Supported by:

    国家自然科学基金(10471010)、天津师范大学教育基金(52LJ80)资助

Abstract:

This paper concerns the problem of the infinite-dimensional σ-widths and optimal recovery of Besov-Wiener classes Spqθr B(Rd) and Spqθr B(Rd) in the metric Lq(Rd) for 1≤ q ≤ p < ∞. By considering the approximation by spline functions and constructing a kind of continuous spline operators, the author obtains the weak asymptotic results concerning the infinite dimensional Kolmogorov widths, the infinite dimensional linear widths, the infinite dimensional Gel'fand widths  and optimal recovery, respectively.

Key words: Besov-Wiener classes, Infinite-dimensional width, Optimal recovery

CLC Number: 

  • 41A55
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