Approximation of a Function and its Derivatives by Entire Functions

Abstract

Abstract A simple proof is given for the fact that for m a non-negative integer, a function f ∊ C (m)(ℝ), and an arbitrary positive continuous function ∊, there is an entire function g such that |g(i)(x) − f (i)(x)| < ∊(x), for all x ∊ ℝ and for each i = 0, 1 …, m. We also consider the situation where ℝ is replaced by an open interval.