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
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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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