再生核空间W_2~1[a,b]W_2~1[c,d]中的最佳插值逼近算子

On the Best Operator of lnterpolation in the Repreducing Kernel Space

构造了一个具有再生核的张量积空间，并利用再生核与算子张量积方法，给出了二元实函数非多项式型最佳插值逼近算子的显式表达式，证明了它对无限加密的矩形网格节点系是一致收敛的，而且误差按空间范数单调下降。

In this paper，a tensor product space which hasreproducing kemel is construted，By the method of reprod ucing kernel and the thesor product of operator，the explioit repasentetion of the best interpolation operdtor for thehiveriate real functions is given，which is no t in polyno minl form，Furthermore，we provethat the proass of rectangular grid knots is thickened infinitely，and that error ofbterpolation decreases monotoniCally，in the sense of space norm when the number ofrectangular grid knots is increased.