English

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