Accession Number : AD0664083

Title :   CONVERGENCE OF COMPLEX LAGRANGE INTERPOLATION POLYNOMIALS WITH NODES LYING ON A PIECEWISE ANALYTIC JORDAN CURVE WITH CUSPS,

Corporate Author : MIAMI UNIV CORAL GABLES FLA DEPT OF MATHEMATICS

Personal Author(s) : O'Hara,P. J. , Jr

Report Date : 1967

Pagination or Media Count : 52

Abstract : Let the analytic and univalent function z = phi(w) map the exterior of absolute value of w = 1 onto the exterior region of a Jordan curve C, so that infinity (opposite pointed arrows) infinity, and let phi be extended so as to give a topological map of absolute value of w = 1 onto C. Let S sub n = (phi(exp 2 pi ik/(n + 1)); k = 0, 1, ..., n) and let f(z) be continuous on C. Let L sub n(f; z) be the polynomial of degree at most n which interpolates to f in the points S sub n. The problem with which this paper is basically concerned is that of proving that with certain restrictions on C which include rectifiability, the equation Lim as n approaches infinity (L sub n(f; z)) = 1/2 pi i the integral over C of the quantity (f(z prime)dz prime/(z prime - z)) holds for z epsilon Int C, and the limit is uniform on any compact subset of Int C.

Descriptors :   (*INTERPOLATION, ANALYTIC FUNCTIONS), (*NUMERICAL ANALYSIS, THEOREMS), POLYNOMIALS, MAPPING(TRANSFORMATIONS), FUNCTIONS(MATHEMATICS), SET THEORY, COMPLEX VARIABLES, BANACH SPACE, SEQUENCES(MATHEMATICS), CONVERGENCE

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE