Completions of normed algebras of differentiable functions

William J. Bland, and Joel F. Feinstein. "Completions of normed algebras of differentiable functions." Studia Mathematica 170.1 (2005): 89-111. <http://eudml.org/doc/284799>.

@article{WilliamJ2005,
abstract = {We look at normed spaces of differentiable functions on compact plane sets, including the spaces of infinitely differentiable functions considered by Dales and Davie in [7]. 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.},
author = {William J. Bland, Joel F. Feinstein},
journal = {Studia Mathematica},
keywords = {normed algebras; differentiable functions; completion; polynomial approximation; rational approximation.},
language = {eng},
number = {1},
pages = {89-111},
title = {Completions of normed algebras of differentiable functions},
url = {http://eudml.org/doc/284799},
volume = {170},
year = {2005},
}

TY - JOUR
AU - William J. Bland
AU - Joel F. Feinstein
TI - Completions of normed algebras of differentiable functions
JO - Studia Mathematica
PY - 2005
VL - 170
IS - 1
SP - 89
EP - 111
AB - We look at normed spaces of differentiable functions on compact plane sets, including the spaces of infinitely differentiable functions considered by Dales and Davie in [7]. 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.
LA - eng
KW - normed algebras; differentiable functions; completion; polynomial approximation; rational approximation.
UR - http://eudml.org/doc/284799
ER -