Timeline for Asymptotic decay rate of an oscillatory integral
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Mar 13, 2020 at 7:54 | vote | accept | Ludwig | ||
| Mar 11, 2020 at 20:03 | answer | added | skbmoore | timeline score: 3 | |
| Feb 26, 2020 at 15:26 | history | edited | Ludwig | CC BY-SA 4.0 |
added 30 characters in body
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| Feb 25, 2020 at 14:28 | comment | added | Ludwig | @WillieWong Yes, you are right. I modified the title. | |
| Feb 25, 2020 at 14:27 | history | edited | Ludwig | CC BY-SA 4.0 |
edited body; edited title
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| Feb 25, 2020 at 14:25 | comment | added | Willie Wong | These are things that you could've included in your question to start with. Frequently when people talk about asymptotics of oscillatory integral they are talking about stationary phase issues. In your case you might as well just titled the question about asymptotic decay rates of the Fourier series. | |
| Feb 25, 2020 at 14:23 | comment | added | B K | As often with parameter-dependent integrals, Feyman's trick (taking derivatives with respect to the parameter $k$) might be useful here. | |
| Feb 25, 2020 at 14:21 | answer | added | Willie Wong | timeline score: 2 | |
| Feb 25, 2020 at 14:13 | history | edited | Ludwig |
edited tags
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| Feb 25, 2020 at 13:57 | comment | added | Ludwig | @WillieWong not sure I understand your point. To clarify, I would like to find an asymptotic estimate of the form $I(n)\sim f(n)$, where $f(n)$ decays exponentially. Numerics suggests that $f(n)=c^{2n}/\sqrt{n}$, where $c=k-\sqrt{k^2-1}$ but I'm looking for a formal proof. | |
| Feb 25, 2020 at 13:52 | comment | added | Ludwig | @WillieWong Yes, correct. However, I would like to explicitly characterize the decay rate of $I(n)$ as a function of parameter $n$. | |
| Feb 25, 2020 at 13:50 | comment | added | Willie Wong | The function $(1-\cos(2x))(1-\cos(2y)) / (2k - \cos x - \cos y)$, by your assumption, is a smooth function on the torus. So its Fourier transform decays faster than any polynomial, no? | |
| Feb 25, 2020 at 13:42 | history | edited | Ludwig | CC BY-SA 4.0 |
changed notation
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| Feb 24, 2020 at 10:06 | history | asked | Ludwig | CC BY-SA 4.0 |