Timeline for Branch cuts, inverse Fourier transform and large time asymptotics
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 18 at 19:15 | comment | added | Mahdiyar | The good old book "Introduction to Fourier analysis and generalized functions" by Lighthill has a section 4.3 titled "The asymptotic expression for the Fourier transform of a function with a finite number of singularities" which addressed this question. | |
| Feb 6, 2022 at 20:37 | history | edited | Fetchinson0234 | CC BY-SA 4.0 |
added 459 characters in body
|
| Feb 6, 2022 at 19:41 | history | edited | Fetchinson0234 | CC BY-SA 4.0 |
added 480 characters in body
|
| Feb 6, 2022 at 19:22 | comment | added | Fetchinson0234 | Correct. The particular form of $F(\omega)$ in that question was not relevant, I'm after a general statement, that's why I deleted that post. The context is basically that I have a very compicated $F(\omega)$ and no way I can do the inverse Fourier transform analytically. But that's okay, I'm only after the large $t$ behavior. So, presumably, one can get $C,a,\nu$ from $F(\omega)$ somehow, without doing the full inverse Fourier transform. I guess if the branch cut of $F(\omega)$ is at $\omega_0$ then $a = - i \omega_0$. I'm pretty sure the general theory is in some (elementary) text book. | |
| Feb 6, 2022 at 19:02 | comment | added | Carlo Beenakker | I presume this is motivated by a question you deleted --- perhaps you can make contact to provide some motivation. | |
| Feb 6, 2022 at 16:08 | history | asked | Fetchinson0234 | CC BY-SA 4.0 |