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- W2223587623 abstract "We say that f is analytic at x0 if T (f, x0) converges to f on an open neighbourhood of x0. If this is not the case, we say that f has a singularity at x0. A function with a singularity at each point of an interval is called nowhere analytic on the interval. Several examples of infinitely differentiable nowhere analytic functions exist and generic results have already been obtained ([2, 3, 5, 6, 7]). This question of genericity can also be treated using the concept of prevalence, introduced by Hunt, Sauer and Yorke ([4]). In the talk, we show that the set of nowhere analytic functions is prevalent in C∞([0, 1]). More precise results are obtained using Gevrey classes ([1]). This study is then extended to the classes of quasi-analytic functions." @default.
- W2223587623 created "2016-06-24" @default.
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- W2223587623 date "2013-05-30" @default.
- W2223587623 modified "2023-09-27" @default.
- W2223587623 title "Prevalence of nowhere analytic functions" @default.
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