vix.ing · top · new · best · stats · spec

Completions of normed algebras of differentiable functions

2003/10/13 by W. J. Bland, William J. Bland, Bland, W. J. +2
Computer Science · Mathematics · #46E10 #46J15 #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Iterative Methods for Nonlinear Equations #Polynomial and algebraic computation #math.FA #msc:46E10 #msc:46J15

paper · pdf · doi:10.48550/arxiv.math/0310181

18 pages LaTeX, one figure

arxiv created 2003/10/13 · openalex publication_date 2003/10/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related