Timeline for Composition of Riesz potentials
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 13, 2018 at 19:00 | history | edited | Piotr Hajlasz | CC BY-SA 4.0 |
added 6 characters in body
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| May 19, 2018 at 13:16 | vote | accept | Piotr Hajlasz | ||
| Mar 28, 2018 at 9:49 | answer | added | Mateusz Kwaśnicki | timeline score: 3 | |
| Mar 27, 2018 at 23:38 | comment | added | Piotr Hajlasz | @MateuszKwaśnicki A very nice argument. You should post it as an answer. | |
| Mar 22, 2018 at 22:38 | comment | added | Mateusz Kwaśnicki | There are many ways to prove this fact. The most elementary one that I know involves the subordination formula $u_\alpha(x) = (\Gamma(\alpha/2))^{-1} \int_0^\infty t^{\alpha/2-1} g_t(x) dx$ (where $g_t(x) = (4 \pi t)^{-n/2} e^{-|x|^2/(4t)}$ is the Gauss–Weierstrass kernel; this formula follows easily from the gamma integral), together with Fubini and $g_t * g_s = g_{t+s}$. Similar argument is typically used to show that the Fourier transform of $u_\alpha$ is indeed $|\xi|^{-\alpha}$ (without multiplication by a constant). | |
| S Mar 22, 2018 at 21:53 | answer | added | Piotr Hajlasz | timeline score: 3 | |
| S Mar 22, 2018 at 21:53 | history | asked | Piotr Hajlasz | CC BY-SA 3.0 |