Nowhere analytic \(C^\infty\) functions (Q1178484)
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scientific article; zbMATH DE number 21704
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nowhere analytic \(C^\infty\) functions |
scientific article; zbMATH DE number 21704 |
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Nowhere analytic \(C^\infty\) functions (English)
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26 June 1992
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The author rediscovers the known theorem of \textit{D. Morgenstern} [Math. Nachr. 12, 74 (1954; Zbl 0058.28902)] according to which the set of \(C^ \infty\) functions with a Pringsheim singularity at each point of the unit interval \(I=[0,1]\) is a comeager subset of \(C^ \infty(I)\). See also \textit{J. Siciak} [Zesz. Nauk. Politech. Śląsk. 853, Mat.-Fiz. 48, 127--146 (1986; Zbl 0777.26020) -- special volume in honour of Professor Zygmunt Zahorski] for a multidimensional version of Morgenstern's theorem.
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Zahorski's theorem
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\(C^\infty\) functions
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Pringsheim singularity
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Morgenstern's theorem
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