Timeline for Does this formula correspond to a series representation of the Dirac delta function $\delta(x)$?
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Mar 19, 2022 at 18:50 | vote | accept | Steven Clark | ||
| Mar 19, 2022 at 18:49 | answer | added | Steven Clark | timeline score: 0 | |
| Jan 6, 2021 at 16:10 | vote | accept | Steven Clark | ||
| Mar 19, 2022 at 18:50 | |||||
| Jan 3, 2021 at 2:42 | answer | added | Steven Clark | timeline score: 0 | |
| Oct 1, 2020 at 16:30 | comment | added | Steven Clark | @user64494 $g(x)\to\delta(x)$ if $\forall\,f(x)\in C^\infty_c(\Bbb{R}), \int_{-\infty}^\infty g(x)f(x)dx\to f(0)$. Most representations of $\delta(x)$ are limit representations (e.g. see formulas 34-40 at mathworld.wolfram.com/DeltaFunction.html and functions.wolfram.com/GeneralizedFunctions/DiracDelta/09). Formula (1) above is of interest to me because it is a series representation. | |
| Sep 30, 2020 at 7:56 | comment | added | user64494 | $$\int_{-\infty}^\infty \delta(x)f(y-x)\,dx$$ makes no sense in traditional math (e.g. see encyclopediaofmath.org/wiki/Generalized_function). | |
| Sep 30, 2020 at 2:33 | history | edited | Steven Clark | CC BY-SA 4.0 |
Corrected the lower integration limit from 0 to minus infinity in the paragraph immediately preceding formula (2).
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| Jul 9, 2020 at 3:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 9, 2020 at 2:40 | answer | added | reuns | timeline score: 3 | |
| Jun 8, 2020 at 20:24 | comment | added | Steven Clark | @Mizar Thanks for your suggestion. I changed the fourier-transform tag to analytic-number-therory. | |
| Jun 8, 2020 at 20:18 | history | edited | Steven Clark |
Changed fourier-transform tag to analytic-number-theory which was suggested by a comment.
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| Jun 8, 2020 at 19:52 | comment | added | Mizar | Since this question mentions the Mertens function, rather than several analysis tags I would tag it as (analytic) number theory | |
| Jun 8, 2020 at 18:42 | history | edited | Steven Clark | CC BY-SA 4.0 |
Minor correction to second to last paragraph.
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| Jun 8, 2020 at 17:38 | history | edited | Steven Clark | CC BY-SA 4.0 |
Added formula (7) and edited the last three paragraphs in an attempt to improve readability and clarify a few points.
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| Jun 2, 2020 at 15:59 | history | edited | Steven Clark | CC BY-SA 4.0 |
Minor edit to correct and simplify second to last paragraph.
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| Jun 2, 2020 at 1:37 | history | edited | Steven Clark | CC BY-SA 4.0 |
Minor edit to formula (1) to make it more consistent with the way I think about this formula.
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| Jun 1, 2020 at 20:38 | history | asked | Steven Clark | CC BY-SA 4.0 |