Timeline for Fourier-positivity of a certain function
Current License: CC BY-SA 4.0
21 events
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| Sep 24, 2021 at 15:59 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 22, 2021 at 23:32 | comment | added | Iosif Pinelis | @GiorgioMetafune : Good point! | |
| Sep 22, 2021 at 20:16 | comment | added | Giorgio Metafune | If $p>1$ the result does not hold. In fact positivity for every $a<b$ is equivalent to $h$ being decreasing or $g$ being positive definite. And this is not true since $g(t)-g(0)$ has a zero of order bigger than 2 at $t=0$ and it is known that such a function would be constant (Bhatia, Positive definite matrices, Corollary 5.5.6) | |
| Sep 22, 2021 at 17:33 | comment | added | Iosif Pinelis | @nerdl : The proof certainly will not work for $p>1$, and I think the result will not hold either. | |
| Sep 22, 2021 at 17:31 | vote | accept | nerdl | ||
| Sep 22, 2021 at 17:29 | comment | added | nerdl | @Iosif Pinelis: Thanks so much! Does the result extend to p>1? | |
| Sep 22, 2021 at 17:25 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 22, 2021 at 17:22 | comment | added | Iosif Pinelis | @fedja : The answer is now complete. | |
| Sep 22, 2021 at 17:19 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 22, 2021 at 17:12 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 22, 2021 at 17:02 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 22, 2021 at 16:51 | comment | added | Iosif Pinelis | @fedja : I have now provided details on the previous comment. | |
| Sep 22, 2021 at 16:50 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 22, 2021 at 16:34 | comment | added | Iosif Pinelis | @fedja : It complements the original question and identifies the difficulty, which can be possibly overcome. | |
| Sep 22, 2021 at 16:30 | comment | added | fedja | Erm... How does this address the original question? :) | |
| Sep 22, 2021 at 15:00 | history | undeleted | Iosif Pinelis | ||
| Sep 22, 2021 at 15:00 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 22, 2021 at 14:02 | history | deleted | Iosif Pinelis | via Vote | |
| Sep 22, 2021 at 14:00 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 22, 2021 at 13:55 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 22, 2021 at 13:44 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |