Timeline for Composition algebra of Gevrey function for $s<1$
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| Apr 22, 2019 at 4:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 23, 2018 at 3:58 | comment | added | BigM | @CPJ thanks for the reference to the original work of Gervey. | |
| Dec 23, 2018 at 3:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
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| Apr 26, 2018 at 21:24 | answer | added | arriopolis | timeline score: 2 | |
| Oct 14, 2015 at 20:21 | history | edited | Bazin | CC BY-SA 3.0 |
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| Oct 14, 2015 at 14:59 | history | edited | Bazin | CC BY-SA 3.0 |
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| Oct 14, 2015 at 14:32 | comment | added | Bazin | @CPJ Thanks for your comment. In fact with $M_n=n^{ns}$, we get $(M_n/n^n)^{1/n}=n^{s-1}$ which is increasing for $s\ge 1$. This suggests that the composition algebra property holds for $s\ge 1$ but not for $s<1$. | |
| Oct 13, 2015 at 7:23 | comment | added | Bazin | @Piero D'Ancona You mean $s'<s$ since the Gevrey space $G^{(s)}$ with the notation above is increasing with $s$, e.g. analytic is $G^{(1)}$ is included in $G^{(2)}$ which contains compactly supported functions. On the other hand, I believe that the answer to the question is positive and is a matter of writing a precise Faà de Bruno formula. | |
| Oct 11, 2015 at 20:31 | comment | added | Piero D'Ancona | If I remember correctly, the answer in general is no. However if you compose a Gevrey function of order s'>s with a Gevrey function of order s you get a Gevrey function of order s. | |
| Oct 11, 2015 at 18:04 | history | edited | Bazin | CC BY-SA 3.0 |
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| Oct 9, 2015 at 16:14 | comment | added | CPJ | There is a result (Cartan?) on Carleman-Denjoy classes saying that they are stable under composition if the sequence $(M_n/n!)^{1/n}$ is increasing. Letting M_n = (n!)^{s}, this should be true. See this paper. Also Gevrey himself seems to have proved that. | |
| Oct 9, 2015 at 15:34 | history | edited | YCor |
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| Oct 9, 2015 at 14:06 | history | edited | Bazin | CC BY-SA 3.0 |
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| Oct 9, 2015 at 13:59 | history | asked | Bazin | CC BY-SA 3.0 |