Some remarks on lacunary interpolation in the roots of unity

The object of this note is to consider the problem of obtaining the explicit representations for polynomials of interpolation in the (0,2,3) case as explained in the introduction. We also show that Dini-Lipschitz condition suffices for the convergence problem, both in this and in the general result of Kis. This paper was completed while the author was at the University of Chicago under Air Force Grant AF-AFOSR-62-118 in the summer of 1962–63. The author is grateful to Professor A. Zygmund and to Professor Turán for several useful suggestions.