实数轴上Gr nwald插值算子的收敛性

Convergence of Gr nwald interpolatory operators on the whole real line.

考虑了拓展插值结点取值范围后的Gr nwald插值算子在实数轴上的收敛性,证明了将结点范围扩大到全实轴后,即取为Hermite多项式的零点,对任意点x∈(-∞,∞),有Gn(f,x)→f(x),n→∞,其中,f(x)为实数轴上任一满足|f(x)|=O(ex2/2)的连续函数.

The convergence of Gr u nwald interpolatory operators is investigated after extending the range of the interpolation points to the whole real line. It is proved that if the zeros of Hermite polynomials are taken as the interpolation nodes, then holds, n→∞, where f(x) is any continuous function on the real line that satisfies |f(x)|=O