Timeline for The supremum value of $\int f(t) \log{\frac{1}{|t|}} \, dt$ for normalized Fourier pairs non-negative outside of $[-1,1]$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 13, 2017 at 4:27 | vote | accept | Vesselin Dimitrov | ||
| Nov 13, 2017 at 3:00 | answer | added | Terry Tao | timeline score: 8 | |
| Nov 13, 2017 at 2:50 | comment | added | Vesselin Dimitrov | @Lucia: Indeed, and also, it is worth adding that this $1.5$ lower bound can be improved. In the special case below the line, this example amounts to taking $g(t) \equiv 1$ on $[0,1]$. If instead we choose there $g(t) := (-30t^2 + 30t + 2)/7$ on $[0,1]$, we get the improved value of $977/588-\log{54/49} = 1.5644\ldots$. (I think this is best possible for a quadratic choice of $g$.) | |
| Nov 13, 2017 at 2:31 | comment | added | Lucia | Just an observation that if $f(x) =\max(0,1-|x|)$ then the integral is $1.5$. So $1+\gamma$ is not far from the answer! | |
| Nov 13, 2017 at 1:52 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
added 1052 characters in body
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| Nov 8, 2017 at 23:13 | history | asked | Vesselin Dimitrov | CC BY-SA 3.0 |