Timeline for Maximum of a mollified/convolution function
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2014 at 7:55 | answer | added | Dirk | timeline score: 1 | |
| Nov 3, 2014 at 19:18 | comment | added | Alexandre Eremenko | It is easy to see that any condition on the mollifier is not sufficient. You need some conditions on $f$ itself. | |
| Nov 3, 2014 at 15:37 | comment | added | Mole | @Dirk Many thanks for the helpful pointer. | |
| Nov 3, 2014 at 15:11 | comment | added | Dirk | Questions like this have been treated in the concept of "scale space methods" in mathematical image processing about 15 or 20 years ago where one was interested in the question: How many local minima and maxima survive after convolution and can new local minima or maxima be created? Unfortunately I forgot about the exact references but one result was along the lines: If you take a scale kernel $\phi_t(x) = 1/t\phi(x/t)$ and require that the number of local maxima and minima of $\phi_t\ast f$ is decaying with $t$, and some more hypotheses, then $\phi$ is a Gaussian… | |
| Nov 3, 2014 at 12:52 | history | edited | Mole | CC BY-SA 3.0 |
edited title
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| Nov 3, 2014 at 10:32 | history | edited | Mole | CC BY-SA 3.0 |
added 36 characters in body
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| Nov 3, 2014 at 10:27 | review | First posts | |||
| Nov 3, 2014 at 10:42 | |||||
| Nov 3, 2014 at 10:24 | history | asked | Mole | CC BY-SA 3.0 |