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    Finitely-Generated Algebras of Smooth Functions, in One Dimension

    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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    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, (
    Keywords: Finitely-Generated Algebras; Smooth Functions; One Dimension;
    Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
    Item ID: 14808
    Identification Number:
    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
    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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