Completions of normed algebras of differentiable functions
Functional Analysis
2007-05-23 v1
Abstract
In this paper we look at normed spaces of differentiable functions on compact plane sets, including the spaces of infinitely differentiable functions originally considered by Dales and Davie. For many compact plane sets the classical definitions give rise to incomplete spaces. We introduce an alternative definition of differentiability which allows us to describe the completions of these spaces. We also consider some associated problems of polynomial and rational approximation.
Keywords
Cite
@article{arxiv.math/0310181,
title = {Completions of normed algebras of differentiable functions},
author = {W. J. Bland and J. F. Feinstein},
journal= {arXiv preprint arXiv:math/0310181},
year = {2007}
}
Comments
18 pages LaTeX, one figure