Hermite-Fejér插值的收敛准则(英文)

Convergence Criteria for Hermite-Fejer Interpolation

中文摘要:

      本文给出Hermite-Fejér插值的若干收敛准则.其中之一是:Hermite-Fejer插值算子对每一个连续函数一致收敛当且仅当该算子范数一致有界且该算子对两个单项式x及x²一致收敛.

英文摘要:

      In this paper we give useful convergence criteria for Hermite-Fejer interpo-lation H_n(f, x) , One of them is: H_n(f,x) converges uniformly to f(x) if and only if the norms of H_n(f,x) are uniformly bounded for all n and H_n(x^k , x) converges uniformly to x^k for k=l,2.