Adaptive widths of the approximation functional on the Sobolev space W_2~r with Gaussian measure  

作　　者：FANG Gensun and YE Peixin(Department of Mathematics, Beijing Normal University, Beijing 100875, China) 

出　　处：《Progress in Natural Science:Materials International》2002年第7期506-511,共6页自然科学进展·国际材料（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 10071006) ; Research Fund for the Doctoral Program Higher Education.

摘　　要：The tight orders for the Kolmogorov and adaptive ( n,ε, δ) -widths of the Sobolev spaces W2γ equipped with a Gaussian measure in the Li-norm and Loo-norm are determined by the method of discretization, which is based on reducing the calculation of the (n,ε, δ)-widths of the Sobolev space to the calculation of (n, ε, δ)-widths of finite-dimensional set equipped with the Gaussian measure.The tight orders for the Kolmogorov and adaptive (n,ε,δ)-widths of the Sobolev spaces Wr2 equipped with a Gaussian measure in the L1-norm and L∞-norm are determined by the method of discretization, which is based on reducing the calculation of the (n,ε,δ)-widths of the Sobolev space to the calculation of (n,ε,δ)-widths of finite-dimensional set equipped with the Gaussian measure.

关 键 词：Kolmogorov (n eeeeeee 777777777)-widths non-adaptive and adaptive Gaussian measure. 

分 类 号：O241[理学—计算数学]