A remark on the approximation theorems of Whitney and Carleman-Scheinberg

Approximation of a Function and its Derivatives by Entire Functions

“…In [9] and [3] the functions to be approximated are defined on the real part R N of C N = R N + iR N and they are approximated by functions holomorphic in all of C N . Very recently, Johanis [7] has considered the more general problem of approximating a function f given on only a portion Ω of R N . Whitney's famous theorem [10] allows one to approximate such functions f by functions analytic on Ω.…”