Acta mathematica scientia,Series B ›› 2003, Vol. 23 ›› Issue (2): 178-.

• Articles • Previous Articles     Next Articles

WIDTHS AND AVERAGE WIDTHS OF SOBOLEV CLASSES

 LIU Yong-Beng, HU Gui-Qiao   

  1. Department of Mathematics, Beijing Normal University, Beijing 100875, China
  • Online:2003-04-07 Published:2003-04-07
  • Supported by:

    1Received October 11, 2000; revised November 10, 2001. The project is supported partly by the National
    Natural Science Foundation of China (10071007) and partly by the Foundation for University Key Teachers by
    the Ministry of Education of China and partly by the Scientific Research Foundation for Returned Overseas
    Chinese Scholars by the Ministry of Education of China
    2The present address of the second author: Department of Mathematics, Tianjing Normal University, Tianjing
    300074, China

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Abstract:

This paper concerns the problem of the Kolmogorov $n$-width, the linear
$n$-width, the Gel'fand $n$-width and the Bernstein $n$-width of Sobolev
 classes of the periodic multivariate functions in the space $L_{\bf p}
(T^d)$ and the average Bernstein $\sz$-width, average Kolmogorov $\sz$-widths,
the average linear $\sz$-widths of Sobolev classes of the multivariate
functions in the space $L_{\bf p}(R^d)
$, where ${\bf p}=(p_1,\cdots,p_d),1\le p_j<\infty,
 j=1,2,\cdots,d,$ or $p_j=\infty, j=1,2,\cdots,d$.
Their weak asymptotic behaviors are established for
 the corresponding quantities.

Key words: Multivariate function, Sobolev class, width, average width

CLC Number: 

  • 41A63
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