LAGRANGE INTERPOLATION IN NON-UNIFORMLY DISTRIBUTED NODES ON THE UNIT CIRCLE
Let / be a function which is holomorphic in the disk DR := { ζ S C : |z| < R } for some R > 1, and let Ln denote the Lagrange interpolatory polynomial of / in the (n + l)-st roots of unity. Then it is well-known that L„(z) —» f ( z ) (n —» oo) locally uniformly in DR. In this note we study the convergence of Lagrange interpolatory polynomials based on nodes which are the images of the roots of unity under a Möbius transformation of the unit disk onto itself. It turns out that these nodes are not uniformly distributed. Furthermore, we consider Walsh equiconvergence of these polynomials. AMS 1980 classification: 30E10