About Nodal Systems for Lagrange Interpolation on the Circle

Abstract

We study the convergence of the Laurent polynomials of Lagrange interpolation on the unit circle for continuous functions satisfying a condition about their modulus of continuity. The novelty of the result is that now the nodal systems are more general than those constituted by the n roots of complex unimodular numbers and the class of functions is different from the usually studied. Moreover, some consequences for the Lagrange interpolation on $[-\mathrm{1,1}]$ and the Lagrange trigonometric interpolation are obtained.