Timeline for L¹ norm of Riesz potentials on flat tori
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 21, 2022 at 15:40 | history | edited | Matt Rosenzweig | CC BY-SA 4.0 |
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| Sep 21, 2022 at 12:27 | comment | added | Matt Rosenzweig | @MateuszKwaśnicki Thanks for your comment, Mateusz! I might be wrong, but I don't think one can directly show the periodization is a convergent series in general, since in the case $s<d$, the Riesz potential on $\mathbb{R}^d$ does not decay fast enough. | |
| Sep 21, 2022 at 10:36 | comment | added | Mateusz Kwaśnicki | If I am not mistaken, $g$ is simply the periodization of the usual RIesz kernel $c_{d,s}|x|^{-s}$. I do not think, though, that a reasonable expression for $\|g\|_1$ is possible when $d \geqslant 2$. Already the description of the set $\{g < 0\}$ is problematic, I believe. And I the logarithmic case $s = 0$ is does not seem any simpler. | |
| Sep 21, 2022 at 2:15 | history | edited | Matt Rosenzweig | CC BY-SA 4.0 |
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| Sep 20, 2022 at 16:12 | history | edited | LSpice | CC BY-SA 4.0 |
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| Sep 20, 2022 at 15:33 | history | asked | Matt Rosenzweig | CC BY-SA 4.0 |