K-functionals on L1 (Rn) related to the Laplacian

被引：0
|
作者：
Trebels, W
Westphal, U
机构：
[1] Tech Univ Darmstadt, Fachbereich Math, D-64289 Darmstadt, Germany
[2] Univ Hannover, Inst Math, D-30167 Hannover, Germany
来源：
HARMONIC ANALYSIS AT MOUNT HOLYOKE | 2003年 / 320卷
关键词：
K-functional; Laplacian on R-n; saturation; moduli of smoothness; approximation processes;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The K-functional with respect to L-1 (R-n) and the domain of the Laplacian Delta in the weak sense in L-1(R-n) (as well as of (-Delta)(alpha/2), alpha > 0,) is characterized in different ways. These characterizations make evident that the K-functional is a perfect interface between the smoothness of a function and the rate of convergence arising when the function is approximated by appropriate linear means. In particular, a short and straightforward proof of a result of Ditzian 1991 is given.
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页码：459 / 465
页数：7
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