ON SOME GENERAL LACUNARY INTERPOLATION PROBLEMS

The object of this paper is to give a unified and complete treatment o f these related cases of lacunary interpolation whose special cases ca n be found scattered in thr literature. We consider only the case when the nodes are thr zeros of pi(n)(X) whose derivative is -n(n - 1) P-n -1(X), the Legendre polynomial of degree n(-1). We find the fundamenta l polynomials and five the convergence result. (C) 1996 Academic Press , Inc.