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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Zero sets of functions from non-quasi-analytic classes


Author: Robert B. Hughes
Journal: Proc. Amer. Math. Soc. 27 (1971), 539-542
MSC: Primary 26.80
Erratum: Proc. Amer. Math. Soc. 39 (1973), 651.
MathSciNet review: 0272965
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Abstract: It is well known that any closed subset of the line is the zero set of a $ {C^\infty }$-function. One can also specify the orders of the zeros at the isolated points. The present paper improves this result by replacing the class of $ {C^\infty }$-functions by any non-quasi-analytic class of $ {C^\infty }$-functions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0272965-4
PII: S 0002-9939(1971)0272965-4
Keywords: Infinitely differentiable functions, quasi-analytic, singular functions, zero set
Article copyright: © Copyright 1971 American Mathematical Society