Timeline for Convolution of $L^2$ functions
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| May 23, 2023 at 19:21 | comment | added | Bazin | @GiorgioMetafune Assuming that $u$ is even and real-valued, you get that the Fourier transform of $u\ast u$ is even and non-negative. Now an analytic non-negative function of one variable is a sum of squares, something which is not true in higher dimensions. Now, in one dimension you can write $u\ast u$ as a finite sum of $u_j\ast u_j$ where each $u_j$ is compactly supported; some details need to be completed, but there is clearly no hope to get something of that type in higher dimensions. | |
| May 21, 2023 at 17:36 | answer | added | Terry Tao | timeline score: 5 | |
| May 20, 2023 at 16:07 | answer | added | Christian Remling | timeline score: 8 | |
| May 20, 2023 at 14:00 | comment | added | Giorgio Metafune | Do you know what happens for $n=1$? | |
| May 19, 2023 at 20:38 | answer | added | Iosif Pinelis | timeline score: 3 | |
| May 19, 2023 at 16:52 | history | edited | YCor |
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| May 19, 2023 at 16:24 | history | asked | Bazin | CC BY-SA 4.0 |