Lagrange interpolation and entire functions

Abstract

For a function f defined almost everywhere on R. Let {Ln (f)} be the sequence of Lagrange interpolation polynomials that approximates f, where the nodes are taken to be the zeros of a certain sequence of orthogonal polynomials. In this paper, we will give a condition on the decay of the error term 16 |f-Ln(f) |, which makes f the restriction on R of an entire function of order one and finite type. In the case of the Hermite polynomials an estimate on the type is given.