Approximation of a Function and its Derivatives by Entire Functions

作者：Gauthier Paul M^*; Kienzle Julie^*

来源：Canadian Mathematical Bulletin, 2016, 59(1): 87-94.

DOI：10.4153/CMB-2015-060-5

• Carleman theorem

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

• 出版日期2016-3