smooth $C^\infty$ anywhere but analytical $C^{\omega}$ nowhere function

Asked May 10 '17 at 19:34

Active May 10 '17 at 19:34

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There is function which is smooth but not analytic in one point. Such as $$f(x)=\exp(-1/x^2)$$

Does there exist function that is smooth $C^\infty$ anywhere but analytical $C^{\omega}$ nowhere ?

If exist, give an explicit example. If not, how to prove?

asked May 10 '17 at 19:34

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See https://math.stackexchange.com/questions/620290/is-it-possible-for-a-function-to-be-smooth-everywhere-analytic-nowhere-yet-tay?rq=1 – Jason May 10 '17 at 19:38
Google it. Alternatively, just search this site. Low effort post. – MathematicsStudent1122 May 10 '17 at 19:38

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