扩充Grnwald插值算子

On Extended Grunwald Interpolatory Operator

该文考虑了基于为ｎ次Ｊａｃｏｂｉ多项式）零点的扩充Ｇｒｕｎｗａｌｄ插值算子，主要证明了扩充Ｇｒｕｎｗａｌｄ插值算子在（－１，１）上内闭一致逼近连续函数且不可能在整个闭区间［－１，１］上一致逼近连续函数，并进一步表明扩充Ｇｒｕｎｗａｌｄ插值算子在Ｌ１范数意义下收敛于连续函数。

The extended Grunwald interpolation based on the zeros of(1-x2)(x)(where) (x) is the n-th Jacobi polynomial and 1/2≤α,β<1) is considered.It ismainly shown that it uniformly converges to the continuous function just on any closed set not on whole interval [-1,1].Moreover,it is shown that it convergesto the continuous function on L1-norm.