Allan, Graham and Kakiko, Grayson and O'Farrell, A.G. and Watson, R.O.
(1998)
Finitelygenerated algebras of smooth functions in one dimension.
Journal of functional Analysis, 158 (2).
pp. 458474.
ISSN 00221236
Abstract
We characterise the closure in C∞,(R, R) of the algebra generated by an arbitrary finite pointseparating set of C∞functions. The description is local, involving Taylor
series. More precisely, a function f ∈ C∞ belongs to the closure of the algebra generated by ψ1,...,ψr as soon as it has the 'right kind' of Taylor series at each point a such that ψ1'(a)...=ψr1 ( a)=0. The 'right kind' is of the form q 0 (T∞a ψ1 ψ1(a), ..., T∞a ψrψr(a)), where q is a power series in r variables, and T a ψi denotes the Taylor series of ψi about a.
Item Type: 
Article

Keywords: 
Taylor series; Smooth functions; Alegebra. 
Academic Unit: 
Faculty of Science and Engineering > Mathematics and Statistics 
Item ID: 
1808 
Depositing User: 
Prof. Anthony O'Farrell

Date Deposited: 
25 Jan 2010 13:33 
Journal or Publication Title: 
Journal of functional Analysis 
Publisher: 
Elsevier 
Refereed: 
Yes 
URI: 

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