A note on approximation of continuous functions on normed spaces

Keywords:
normed space, continuous function, analytic function, -analytic function, uniform approximation, separating polynomial
Published online:
2020-06-12
Abstract
Let be a real separable normed space admitting a separating polynomial. We prove that each continuous function from a subset of to a real Banach space can be uniformly approximated by restrictions to of functions, which are analytic on open subsets of . Also we prove that each continuous function to a complex Banach space from a complex separable normed space, admitting a separating -polynomial, can be uniformly approximated by -analytic functions.
How to Cite
(1)
Mytrofanov, M.; Ravsky, A. A Note on Approximation of Continuous Functions on Normed Spaces. Carpathian Math. Publ. 2020, 12, 107-110.