Timeline for Factoring Bessel functions into an amplitude and a phase
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| S Nov 20, 2019 at 7:18 | history | bounty ended | Vladimir Reshetnikov | ||
| S Nov 20, 2019 at 7:18 | history | notice removed | Vladimir Reshetnikov | ||
| Nov 17, 2019 at 14:06 | comment | added | FusRoDah | It cannot be done for the Airy function, I suppose. If you write $y=Ae^{i\phi}$ for a solution of $\frac {d^2y}{dx^2} \pm xy=0$, you get two equations for $A$ and $\phi$, by equating real and imaginary parts. One of them is $2A'\phi '+A\phi ''=0$. But this cannot hold if the functions are completely monotone, because the left side would be positive and thus not $0$. | |
| Nov 17, 2019 at 11:42 | answer | added | Mateusz Kwaśnicki | timeline score: 2 | |
| Nov 17, 2019 at 11:01 | answer | added | juan | timeline score: 2 | |
| S Nov 17, 2019 at 9:12 | history | bounty started | Vladimir Reshetnikov | ||
| S Nov 17, 2019 at 9:12 | history | notice added | Vladimir Reshetnikov | Draw attention | |
| May 10, 2016 at 18:18 | comment | added | Vladimir Reshetnikov | @CarloBeenakker Thanks. Yes, I recall seeing this representation in some paper. This might be the representation I am looking for. But the question remains: are those amplitude and phase functions completely monotonic (the paper says just they are simply monotonic), and whether such a factorization unique. | |
| May 10, 2016 at 9:43 | comment | added | Carlo Beenakker | I presume this is not the amplitude/phase factorization you are looking for? | |
| May 9, 2016 at 22:53 | history | edited | Vladimir Reshetnikov | CC BY-SA 3.0 |
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| May 9, 2016 at 22:35 | history | edited | Vladimir Reshetnikov | CC BY-SA 3.0 |
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| May 9, 2016 at 22:25 | history | asked | Vladimir Reshetnikov | CC BY-SA 3.0 |