Allan, Graham and Kakiko, Grayson and O'Farrell, Anthony G. and Watson, R.O. (1998) Finitely-Generated Algebras of Smooth Functions, in One Dimension. Journal of functional Analysis, 158. pp. 458-474. ISSN 0022-1236

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Abstract

We characterise the closure inC∞(, ) of the algebra generated by an arbitrary finite point-separating set ofC∞functions. The description is local, involving Taylor series. More precisely, a functionf∈C∞belongs to the closure of the algebra generated byψ1, …, ψras soon as it has the “right kind” of Taylor series at each pointasuch thatψ′1(a)=…=ψ′r(a)=0. The “right kind” is of the formq∘(T∞aψ1−ψ1(a), …, T∞aψr−ψr(a)), whereqis a power series inrvariables, andT∞aψidenotes the Taylor series ofψiabouta.

Item Type:	Article
Additional Information:	Cite as: Graham Allan, Grayson Kakiko, A.G O'Farrell, R.O Watson, Finitely-Generated Algebras of Smooth Functions, in One Dimension, Journal of Functional Analysis, Volume 158, Issue 2, 1998, Pages 458-474, ISSN 0022-1236, https://doi.org/10.1006/jfan.1998.3250. (https://www.sciencedirect.com/science/article/pii/S0022123698932505)
Keywords:	Finitely-Generated Algebras; Smooth Functions; One Dimension;
Academic Unit:	Faculty of Science and Engineering > Mathematics and Statistics
Item ID:	14808
Identification Number:	https://doi.org/10.1006/jfan.1998.3250
Depositing User:	Prof. Anthony O'Farrell
Date Deposited:	08 Sep 2021 13:16
Journal or Publication Title:	Journal of functional Analysis
Publisher:	Elsevier
Refereed:	Yes
URI:	Publisher
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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