Timeline for Where to find a table of fair Fourier transforms? [closed]
Current License: CC BY-SA 4.0
17 events
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| Dec 5, 2018 at 9:16 | history | closed |
Yemon Choi Chris Godsil Stefan Waldmann Mark Wildon მამუკა ჯიბლაძე |
Needs details or clarity | |
| Dec 5, 2018 at 9:16 | comment | added | მამუკა ჯიბლაძე | @reuns It would be more accurate to say that it is not reasonable to expect from somebody composing tables of Fourier transforms to be aware of needs of somebody who is trying to use Fourier transform tables for inventing environments giving sense to $\delta(0)$. | |
| Nov 29, 2018 at 4:50 | review | Close votes | |||
| Dec 5, 2018 at 9:16 | |||||
| May 6, 2018 at 13:04 | history | edited | Anixx | CC BY-SA 4.0 |
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| Jul 6, 2017 at 17:00 | comment | added | reuns | no because $\delta(0)$ doesn't make sense. | |
| Jul 6, 2017 at 9:23 | comment | added | Anixx | @reuns I am now doing things, where $\delta(0)$ makes sense, that's why I need expressions that handle this case correctly. | |
| Jul 6, 2017 at 8:18 | answer | added | cart | timeline score: 6 | |
| Jul 6, 2017 at 6:00 | comment | added | reuns | @Anixx $\delta(0)$ doesn't make sense. The Dirac delta $\delta$ is a distribution defined by $$\int_{-\infty}^\infty \delta(x) f(x)dx = \lim_{\epsilon \to 0^+} \int_{-\infty}^\infty \frac{1_{|x| < \epsilon}}{2 \epsilon} f(x)dx$$ Also $\delta(x)1_{|x| > a}$ is the zero distribution, so it is fairly represented by the zero function. But this doesn't work in the neighborhood of $x=0$. | |
| Jul 6, 2017 at 2:25 | history | edited | Anixx | CC BY-SA 3.0 |
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| Jul 6, 2017 at 2:13 | history | edited | Anixx | CC BY-SA 3.0 |
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| Jul 6, 2017 at 1:25 | history | edited | Anixx | CC BY-SA 3.0 |
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| Jul 6, 2017 at 1:17 | history | edited | Anixx | CC BY-SA 3.0 |
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| Jul 6, 2017 at 1:10 | history | edited | Anixx | CC BY-SA 3.0 |
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| Jul 6, 2017 at 1:08 | answer | added | paul garrett | timeline score: 3 | |
| Jul 6, 2017 at 0:57 | comment | added | Anixx | @Christian Remling I am mostly interested in values of Fourier transforms at $w=0$. At this point I expect $\theta(x+a)$ to produce $a+\pi \delta (0)$. That is a value dependent on $a$. Those expressions from the tables may be OK outside $w=0$ but at this point their behavior is wrong. | |
| Jul 6, 2017 at 0:53 | comment | added | Christian Remling | This is a bit like saying I'm greatly dissatisfied with Dante because I do not read Italian. The results you quote are perfectly valid if interpreted properly, but they do assume theory you apparently haven't studied yet that extends the FT far beyond $L^1$ (tempered distributions). | |
| Jul 6, 2017 at 0:37 | history | asked | Anixx | CC BY-SA 3.0 |