On the filtered polynomial interpolation at Chebyshev nodes

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 in spaces of locally continuous functions equipped weighted uniform norms, the related Lebesgue constants have be uniformly bounded. previous works this has already been proved under different sufficient conditions. Here, we complete study stating also necessary conditions it. Several numerical experiments are given test theoretical results and make comparisons Lagrange same nodes.