The Problem of Timan on the Precise Order of the Best Approximations of Multivariate Functions
Received:October 23, 1997  
Key Words: modulus of continuity   best appraximation   entire function of exponential sphesrical type σ.  
Fund Project:Supported by the National Natrual Science Foundation of China (No.19671012) and by the Doctoral Programme Foundation of Institution of Higher Education of Country Education Committee of China
Author NameAffiliation
KANG Shu-gui Dept. of Math., Beijing Normal University, 100875, China 
LIU Yong-ping Dept. of Math., Beijing Normal University, 100875, China 
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Abstract:
      The problem of Timan on finding a necessary and sufficient condition for Ωk(f，1/σ)Lp(Rn)=O(Aσ(f)Lp(Rn))，σ→∞, is solved. The condition is that Qk(f，δ)Lp(Rn)=O(Ωk+1(f，δ)Lp(Rn))，δ→0.
Citation:
DOI:10.3770/j.issn:1000-341X.2001.02.004
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