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Allan, Graham, Kakiko, Grayson, O'Farrell, A.G. and Watson, R.O. (1998) Finitely-generated algebras of smooth functions in one dimension. Journal of functional Analysis, 158 (2). pp. 458-474. ISSN 0022-1236
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Abstract
We characterise the closure in C∞,(R, R) of the algebra generated by an arbitrary finite point-separating 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 ψr-ψr(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 |
| Related URLs: | |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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