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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Zero sets of functions from non-quasi-analytic classes


Author: R. B. Darst
Journal: Proc. Amer. Math. Soc. 40 (1973), 543-544
MSC: Primary 26A93
DOI: https://doi.org/10.1090/S0002-9939-1973-0323978-7
MathSciNet review: 0323978
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Abstract: Any closed subset $ E$ of the real numbers $ R$ is the zero set of some $ {C^\infty }$-function $ f$. One can also specify the order $ d(s)$ of the zero of $ f$ at each element $ s$ of the set $ S$ of isolated points of $ E$. The present note improves this result by showing that each non-quasi-analytic class $ C\{ {M_n}\} $ contains such functions.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0323978-7
Keywords: $ {C^\infty }$-functions, non-quasi-analytic classes, zero sets
Article copyright: © Copyright 1973 American Mathematical Society

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