W空间中有界线性泛函的最佳逼近

The Best Approximating of Bounded Linear Functional in the Space W

在Ｗ空间中，对Ｗ上的有界线性泛函Ｌ，当已知｛ｕ（ｘｉ，ｙｉ）｝ｎ１时，给出了如下形式Ｌｎ（ｕ）＝ｎｉ＝１ｗｉｕ（ｘｉ，ｙｉ）的最佳逼近Ｌｎ．当｛（ｘｉ，ｙｉ）｝∞１在Ω＝［ａ，ｂ］×［ｃ，ｄ］中稠密时，有ｌｉｍｎ→∞‖Ｌ－Ｌｎ‖＝０．由此得到数值积分公式．

In this paper, we give the best approximating  n for {(x i,y i} n 1Ω=× of following form L n(u)=ni=1w iu(x i,y i),u∈W of bounded linear functional L in the space W. If {(x i,y i)} ∞ 1 is dease on Ω, then we have  lim n→∞‖L- n‖=0.