Timeline for Analyticity of $f*g$ with $f$ and $g$ smooth on $\mathbb{R}$ and analytic on $\mathbb{R}^*$
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| S Jul 7 at 19:05 | history | bounty ended | CommunityBot | ||
| S Jul 7 at 19:05 | history | notice removed | CommunityBot | ||
| Jul 4 at 14:55 | vote | accept | NancyBoy | ||
| Jul 4 at 14:07 | history | edited | LSpice | CC BY-SA 4.0 |
While this is on the front page, typo; removed "thank you"
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| Jul 4 at 9:46 | answer | added | Bazin | timeline score: 10 | |
| Jul 3 at 3:35 | comment | added | RobPratt | Cross-posted: math.stackexchange.com/questions/4940919/… | |
| Jul 2 at 20:11 | history | edited | NancyBoy | CC BY-SA 4.0 |
Simplifying conditions
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| S Jun 29 at 17:46 | history | bounty started | NancyBoy | ||
| S Jun 29 at 17:46 | history | notice added | NancyBoy | Draw attention | |
| Jun 15 at 8:55 | comment | added | Igor Khavkine | @WillieWong Ah yes, a perfectly valid point! | |
| Jun 15 at 0:02 | comment | added | Willie Wong | @IgorKhavkine: $\mathbb{R}$ has two "ends", I can easily imagine a situation where $f$ has exponential decay on one end and $g$ on the other. | |
| Jun 14 at 17:37 | history | edited | LSpice | CC BY-SA 4.0 |
Title
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| Jun 14 at 10:20 | comment | added | Igor Khavkine | The precise condition quoted in the answer by Nate Eldredge uses the $L^2$-norm on the shifted real axis. Consult the cited reference for more details. More specialized literature might give analogous results with different norms. | |
| Jun 14 at 10:07 | comment | added | NancyBoy | Thank you @IgorKhavkine for the post you mentinned. A quick question, when it is mentionned "the fourier transform should decay exponentially", we are talking about the module of the fourier tranform ?. It is to say that if $|\mathcal{F}[f*g](u)| < e^{-a|u|}$ for some $a>0$, $f*g$ is analytic ? | |
| Jun 14 at 9:07 | comment | added | Igor Khavkine | Have a look at the properties of the Fourier transform of analytic functions at MO23679. If you pick your functions to be analytic at least in some strip around the real axis, I suspect that the answer will come out: iff one of $f$ or $g$ is analytic. | |
| Jun 14 at 8:27 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
fixed latex in title
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| Jun 14 at 7:56 | history | asked | NancyBoy | CC BY-SA 4.0 |