Timeline for Explicit computation related to the fractional Laplacian
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 27, 2021 at 21:13 | comment | added | Mateusz Kwaśnicki | Sorry for the delay. I tried to understand what the double integral really means, and I failed. If we integrate it over $x$, this seems to give the quadratic form corresponding to $(-\Delta)^{2s}$ (with $2s$ rather than $s$ in the exponent), which seems slightly odd. I'm afraid I cannot help much here, but if I may ask, out of curiosity: how did you come up with this expression? And why do you expect the claim to be true? I think I must be missing something obvious here. | |
| Mar 25, 2021 at 6:22 | comment | added | Zac | @MateuszKwaśnicki Ok, thanks! Please, let me know | |
| Mar 24, 2021 at 13:03 | comment | added | Mateusz Kwaśnicki | Ah, I realise I did not read your question correctly. Let me think for a minute. | |
| Mar 24, 2021 at 12:20 | comment | added | Zac | @MateuszKwaśnicki Thank you! What if I add another assumption, for example that $(-\Delta)^s u = 1$? | |
| Mar 24, 2021 at 12:09 | comment | added | Mateusz Kwaśnicki | Of course not! Take any smooth $u_0$ with compact support. Then the integral is finite, and so $u = \lambda u_0$ for an appropriate $\lambda$ has the integral equal to $C$, but it is not of the desired form. | |
| Mar 24, 2021 at 12:04 | history | asked | Zac | CC BY-SA 4.0 |