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Finitely-Generated Algebras of Smooth Functions, in One Dimension

✍ Scribed by Graham Allan; Grayson Kakiko; A.G O'Farrell; R.O Watson

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
264 KB
Volume
158
Category
Article
ISSN
0022-1236

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✦ Synopsis

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 1 , ..., r as soon as it has the right kind'' of Taylor series at each point a such that $ 1 (a)= } } } = $ r (a)=0. The right kind'' is of the form q b (T a 1 & 1 (a), ..., T a r & r (a)), where q is a power series in r variables, and T a i denotes the Taylor series of i about a.

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