扩充Hermite-Fejér插值的一个平均收敛定理

The Theorem of Extended Hermite-Fejer Interpolation for Mean Covergence

讨论以一般权函数的正交Ｊａｃｏｂｉ多项式的零点为插值节点的ＥｘｔｅｎｄｅｄＨｅｒｍｉｔｅ－Ｆｅｊéｒ插值算子在Ｌｐｕ空间的平均收敛定理，给出了定理收敛的充分条件．

Weighted Lp mean convergence of Extended Hermite-Fejer operators based on the zeros of orthogonal polynomials with respct to the general weight and Jacobi weight is investigated. Sufficient conditions for such convergence for all continuous functions are given.