The paper deals with a special filtered approximation method, which originates interpolation polynomials at Chebyshev zeros by using de la Vallée Poussin filters. In order to get an optimal approximation in spaces of locally continuous functions equipped with weighted uniform norms, the related Lebesgue constants have to be uniformly bounded. In previous works this has already been proved under different sufficient conditions. Here, we complete the study by stating also the necessary conditions to get it. Several numerical experiments are also given to test the theoretical results and make comparisons to Lagrange interpolation at the same nodes.

本文讨论了一种特殊的滤波近似方法，该方法通过使用de laValléePoussin滤波器在Chebyshev零点处生成插值多项式。为了在配备有加权统一范数的局部连续函数的空间中获得最佳逼近，相关的勒贝格常数必须统一有界。在以前的工作中，已经在不同的充分条件下证明了这一点。在这里，我们通过说明获得该研究的必要条件来完成研究。还进行了一些数值实验，以测试理论结果并与同一节点上的Lagrange插值进行比较。