Timeline for Possible gaps for a function and its Fourier transform
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Nov 30 at 11:01 | history | bounty ended | CommunityBot | ||
| S Nov 30 at 11:01 | history | notice removed | CommunityBot | ||
| S Nov 22 at 9:16 | history | bounty started | kaleidoscop | ||
| S Nov 22 at 9:16 | history | notice added | kaleidoscop | Draw attention | |
| Nov 20 at 11:44 | comment | added | kaleidoscop | Sorry, what I meant by "vanishes on a gap for each coordinate" came out completely wrong, I actually meant that it should vanish on infinite vertical and horizontal gaps, the post edited. | |
| Nov 20 at 11:43 | history | edited | kaleidoscop | CC BY-SA 4.0 |
miswrote the assumption
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| Nov 20 at 11:07 | comment | added | Gro-Tsen | Now I'm even more confused. Vanishing on $O\times O'$ with $O,O'$ nonempty open sets of $\mathbb{R}$ just means the same as vanishing on a nonempty open set of $\mathbb{R}^2$, since the former are a basis of the latter; and anyway the half-plane we're talking about is of the form $\mathbb{R} \times \mathbb{R}_{\gt 0}$. What more do you want? | |
| Nov 20 at 10:55 | comment | added | kaleidoscop | Yes but vanishing on OxO' is stronger (or at least different) than vanishing on a half plane | |
| Nov 20 at 10:50 | comment | added | Gro-Tsen | I don't understand your question: Christian Remling's comment which you referred to points out that if $g$ and $\hat h$ both vanish on a half-line, then $f(x,y) := g(x)\,h(y)$ vanishes on a half-plane and $\hat f$ also does. But vanishing on a half-plane is stronger than vanishing on a quarter-plane, so it seems to me that this $f$ exactly answers the question of your last paragraph. | |
| Nov 20 at 9:14 | history | asked | kaleidoscop | CC BY-SA 4.0 |