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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: 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.

References [Enhancements On Off] (What's this?)

  • [1] S. Mandelbrojt, Analytic functions and classes of infinitely differentiable functions, Rice Inst. Pamphlet 29 (1942), no. 1, 142. MR 0006354
  • [2] Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210528

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Keywords: Infinitely differentiable functions, quasi-analytic, singular functions, zero set
Article copyright: © Copyright 1971 American Mathematical Society