基于Jacobi多项式零点的拟Grünwald插值算子

Quasi-Grünwald interpolation base on the zeros of the Jacobi polynomials

考虑基于一般Jacobi多项式Jn(x)=J(α,β)n(x)(0≤α,β<1)零点∪{-1,1}的拟Grünwald插值多项式G*n(f,x),证明了G*n(f,x)在(-1,1)内几乎一致收敛于连续函数f(x),并给出点态逼近估计.

The Quasi-Grünwald interpolation base on the zeros of the Jacobi polynomials is considered .It shows that Quasi-Grünwald polynomials converge uniformly to the continous function on any closed subinterval of \. The corresponding pointwise approximation estimates are given.The results of \ are extended.