Timeline for Zeros of functions of the form $F(z) = \int_I g(t-z) f(t) \, dt$ with $g$ entire and $f \in L^1(I)$
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| S Jan 26, 2022 at 12:01 | history | bounty ended | CommunityBot | ||
| S Jan 26, 2022 at 12:01 | history | notice removed | CommunityBot | ||
| S Jan 18, 2022 at 10:51 | history | bounty started | Muzi | ||
| S Jan 18, 2022 at 10:51 | history | notice added | Muzi | Authoritative reference needed | |
| Jan 9, 2022 at 20:52 | comment | added | Shannon Starr | In your special example, I do not think it is important that $f$ is compactly supported since you are just using the fact that $g$ is band limited. If $F$ decays quickly enough you may still apply the Poisson summation formula for cases other than your special case. But without the band limited assumption for $F$ you are not recovering $\widehat{F}$ from the sample of $F$ on $\mathbb{Z}$. | |
| Jan 8, 2022 at 17:50 | comment | added | Muzi | you're right, I changed it, thanks! | |
| Jan 8, 2022 at 17:50 | history | edited | Muzi | CC BY-SA 4.0 |
deleted 105 characters in body; edited title
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| Jan 8, 2022 at 17:10 | comment | added | Michael Hardy | If $\mu=g\,dt$ and $ F(z) = \int_I g(t-z) \, d\mu(t),$ then why not write $ F(z) = \int_I g(t-z) g(t)\,dt$ and dispense with the notation involving $\mu \text{ ?} \qquad$ | |
| Jan 8, 2022 at 17:08 | history | edited | Michael Hardy | CC BY-SA 4.0 |
fixing a typo
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| Jan 8, 2022 at 17:03 | history | edited | Muzi | CC BY-SA 4.0 |
added 3 characters in body
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| Jan 8, 2022 at 14:55 | history | edited | Muzi | CC BY-SA 4.0 |
added 70 characters in body
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| Jan 8, 2022 at 13:47 | history | asked | Muzi | CC BY-SA 4.0 |