Timeline for What can be said about the Fourier transforms of characteristic functions?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 13, 2014 at 23:35 | comment | added | Joni Teräväinen | You are right. I am fairly certain though that there should be an unbounded set of finite measure whose Fourier transform is not analytic. | |
| Sep 12, 2014 at 1:49 | comment | added | Nick Strehlke | This is by now a rather old question, but I thought it might be worth pointing out that, in fact, $\hat{\mathbb 1}_A$ does extend to an entire function when $A$ is bounded. This is part of the Paley-Wiener family of results. The problem with the uniform approximation argument is that the convergence $\hat{s}_k\to\hat{f}$ takes place in $L^\infty(\mathbb R^n)$ and not in $L^\infty(\mathbb C^n)$. | |
| Apr 25, 2014 at 11:09 | history | edited | Joni Teräväinen | CC BY-SA 3.0 |
Added references
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| Apr 24, 2014 at 9:40 | history | edited | Joni Teräväinen | CC BY-SA 3.0 |
fixed typo
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| Apr 23, 2014 at 18:30 | history | answered | Joni Teräväinen | CC BY-SA 3.0 |