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Proceedings of the American Mathematical Society

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Localization properties of basic classes of $ C\sp{\infty }$-functions


Author: R. B. Darst
Journal: Proc. Amer. Math. Soc. 46 (1974), 24-28
MSC: Primary 26A93
DOI: https://doi.org/10.1090/S0002-9939-1974-0346113-9
MathSciNet review: 0346113
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Abstract: Suppose that each of $ \mathfrak{M} = C\{ {M_n}\} $ and $ \mathcal{K} = C\{ {K_n}\} $ is a basic class of $ {C^\infty }$-functions defined on $ I = [0,2\pi ]$ and $ \mathfrak{M}$ is not a subset of $ \mathcal{K}$. Then it is shown that $ \mathfrak{M}$ contains functions which are nowhere locally in $ \mathcal{K}$. One of the corollaries asserts that there are quasi-analytic functions which are nowhere locally analytic. It is also shown that many non-quasi-analytic classes contain functions which are nowhere locally quasi-analytic.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0346113-9
Keywords: Analytic functions, $ {C^\infty }$-functions, quasi-analytic functions
Article copyright: © Copyright 1974 American Mathematical Society

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