Timeline for Estimate a Fourier Transform [closed]
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2016 at 16:55 | history | closed |
Willie Wong Wolfgang Ryan Budney Daniel Moskovich Sebastian Goette |
Not suitable for this site | |
| Apr 12, 2016 at 18:24 | answer | added | Fan Zheng | timeline score: 0 | |
| Apr 12, 2016 at 15:52 | history | edited | Stefan Kohl♦ |
Added top-level tag.
|
|
| Apr 12, 2016 at 13:28 | review | Close votes | |||
| Apr 13, 2016 at 16:55 | |||||
| Apr 12, 2016 at 13:14 | comment | added | Willie Wong | @OP: Do you know how to prove it for $N = 0$? (As Asaf said, this is just the standard decay estimate for Fourier transforms of smooth functions.) For $N \neq 0$, you get it by the formula that frequency modulation in physical space equals translation in Fourier space. E.g. en.wikipedia.org/wiki/Fourier_transform#Basic_properties (So in the end I also agree with Asaf that this should be asked on Math.SE instead.) | |
| Apr 12, 2016 at 13:10 | comment | added | Willie Wong | @Asaf: $N_1$ is a vector in $\mathbb{R}^2$, so is $\omega$, the frequency. And also, I think implicitly the constant depends on $h$ and $g$, but not on $N$; otherwise as you indicated the estimate is entirely trivial. | |
| Apr 12, 2016 at 8:31 | comment | added | Asaf | I don't understand what is $N_{1}$ (is that even a number? I'll take that as a constant number), and notice that $C=C(M,f)$ (this is written implicitly in your estimate), therefore the asymptotic expression is true because $f$ is smooth. As the lower modes are controllable by the integral of $f$, you can use this implicit $C_{M,f}$ to have control via the inequality also in the lower modes. Anyhow this is far from being a research question, and should be posted to mathstack. | |
| S Apr 12, 2016 at 1:38 | history | suggested | Tobias Fritz | CC BY-SA 3.0 |
improved formatting
|
| Apr 12, 2016 at 1:27 | comment | added | Tobias Fritz | I've improved the formatting a bit; the question is still the same. | |
| Apr 12, 2016 at 1:25 | review | Suggested edits | |||
| S Apr 12, 2016 at 1:38 | |||||
| Apr 12, 2016 at 1:08 | review | First posts | |||
| Apr 12, 2016 at 1:27 | |||||
| Apr 12, 2016 at 1:05 | history | asked | W.314 | CC BY-SA 3.0 |