Timeline for Fourier Transform ; half space elliptic baby problem
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 15, 2020 at 21:37 | comment | added | Math604 | thanks for your comments; it really helps me. | |
| Dec 15, 2020 at 21:33 | comment | added | Mateusz Kwaśnicki | If you consider zero boundary condition only, you can extend your solution via $u(x,-y) = -u(x,y)$ and then use Fourier transform in all of $\mathbb{R}^2$. This tells you that all solutions that are tempered distributions (jointly) are harmonic polynomials. | |
| Dec 15, 2020 at 21:31 | comment | added | Mateusz Kwaśnicki | I bet there is a way, but I doubt it is very simple: it has to include all sorts of other "exotic" harmonic functions, such as $xy$, $3 x^2 y - y^3$ and so on. (And if you go beyond tempered distributions, then also $\operatorname{Im} \exp((x + i y)^2)$ and so on). | |
| Dec 15, 2020 at 21:21 | comment | added | Math604 | i assume you mean it can be 'worse' like the explicit example i gave. I still thought it should `pop' out of the formula ? No ? | |
| Dec 15, 2020 at 20:55 | comment | added | Mateusz Kwaśnicki | The Fourier transform of $\phi$ need not be a pure function. | |
| Dec 15, 2020 at 20:46 | history | asked | Math604 | CC BY-SA 4.0 |