Timeline for When does a nonnegative $C^1$ function on $[a,b]$ have finitely many zeros?
Current License: CC BY-SA 4.0
10 events
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| Feb 17, 2021 at 2:48 | comment | added | Terry Tao | Analyticity is pretty much the largest regularity class that avoids bump functions. Gevrey classes, for instance, are the most popular class used between the smooth and analytic classes, and they support bump functions also. en.wikipedia.org/wiki/Gevrey_class | |
| Feb 17, 2021 at 1:37 | history | rollback | user168590 |
Rollback to Revision 2
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| Feb 17, 2021 at 1:37 | history | edited | user168590 | CC BY-SA 4.0 |
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| Feb 17, 2021 at 1:36 | comment | added | Jochen Glueck | @WillieWong and user168590: And then, by induction, ... :-) | |
| Feb 17, 2021 at 1:36 | history | edited | user168590 | CC BY-SA 4.0 |
added 43 characters in body
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| Feb 17, 2021 at 1:35 | comment | added | user168590 | @JochenGlueck Sorry, I meant analytic $\mathbb R \to \mathbb R$ and then study the zeros on $[a,b]$. | |
| Feb 17, 2021 at 1:34 | comment | added | Jochen Glueck | I think one has to be a bit careful about your first sentence. What precisely do you mean by analyticity on a closed set? | |
| Feb 17, 2021 at 1:32 | comment | added | user168590 | @WillieWong Or more generally, one condition is that $f'$ has finitely many zeros. | |
| Feb 17, 2021 at 1:29 | comment | added | Willie Wong | How about "$f$ is strictly monotone"? | |
| Feb 17, 2021 at 1:25 | history | asked | user168590 | CC BY-SA 4.0 |