Approximation of a Function and its Derivatives by Entire Functions. Issue 1 (1st March 2016) - Gauthier, Paul M.; Kienzle, Julie
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.