A division's theorem on some class of C^∞-functions

2011/10/03 by Mouttaki Hlal, Hlal, Mouttaki
Mathematics · #26E10 #32B05 #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #Mathematical and Theoretical Analysis #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1110.0281

openalex publication_date 2011/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E_n be the ring of the germs of C^∞-functions at the origin in \Rⁿ. It is well known that if I is an ideal of E_n, generated by a finite number of germs of analytic functions, then I is closed. In this paper we consider an ideal of E_n generated by a finite number of germs in some class of C^∞-functions that are not analytic in à, but quasi-analytic and we shall prove that the result holds in this general situation. We remark that the result is not true for a general ideal of finite type of E_n.

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