Timeline for Interpretation of the singular integral for the definition of fractional Laplacian in classical case $s=1$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 4 at 22:02 | answer | added | Jingeon An-Lacroix | timeline score: 1 | |
| Feb 4 at 19:46 | vote | accept | Jingeon An-Lacroix | ||
| Feb 4 at 18:26 | answer | added | Carlo Beenakker | timeline score: 1 | |
| Feb 4 at 16:15 | comment | added | Christian Remling | This can be made sense of if one first view $f(x)=1/|x|^3$ as a distribution on $\mathbb R\setminus \{ 0\}$. There are various methods to extend this to a distribution on $\mathbb R$, discussed at length in Section 3.2 of Hormander I. Formula (3.2.17') relates these to $\delta''$, which is exactly what you want as $\delta''*u=\delta*u''=u''$. | |
| Feb 4 at 15:45 | history | edited | Christian Remling | CC BY-SA 4.0 |
added 5 characters in body
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| Feb 4 at 11:29 | comment | added | Jingeon An-Lacroix | I was missing the dependence on the constant $c_s$ in the limit of $s\rightarrow 1-$. I think it can be understood that $c_s/|x|^{1+2s}\rightarrow \delta_0''$ in distribution, in the limit of $s\rightarrow 1-$, up to some constant. | |
| Feb 4 at 1:35 | history | asked | Jingeon An-Lacroix | CC BY-SA 4.0 |