Timeline for On the Fourier-Laplace transform of compactly supported distributions
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 20, 2018 at 10:37 | vote | accept | Giulia S-A. | ||
| Sep 19, 2018 at 15:45 | answer | added | Mizar | timeline score: 2 | |
| Sep 19, 2018 at 13:16 | comment | added | Nate Eldredge | @TaQ: All I meant by "pointwise convergence is for free" was the trivial observation that we have $\widehat{f_n}(x) \to \widehat{f}(x)$ for each $x$, simply because $\widehat{f_n}(x) = \langle f_n, e^{i x \cdot}\rangle$. I did not think as far ahead as you got. It'd be great if you would post it as an answer. | |
| Sep 19, 2018 at 8:11 | comment | added | TaQ | @NateEldredge How is "X-wise convergence is for free" defined? If one knows (x) that elements in a bounded set in $\mathscr E'(\mathbb R)$ have "uniformly bounded" supports and orders, then the assertion follows trivially from formula (2) $\ |f(z)|\le\gamma\,(1+|z|)^N{\rm e}^{\,r|\rm{Im}\,z|} $ in the statement of the Paley−Wiener theorem in Rudin's Functional Analysis (Th. 7.23, p. 183 in my edition). Is (x) "for free"? | |
| Sep 19, 2018 at 5:52 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
typo in the title
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| Sep 18, 2018 at 9:01 | vote | accept | Giulia S-A. | ||
| Sep 20, 2018 at 10:37 | |||||
| Sep 18, 2018 at 6:46 | answer | added | Jochen Wengenroth | timeline score: 5 | |
| Sep 18, 2018 at 0:15 | comment | added | Nate Eldredge | Initial thoughts: Pointwise convergence is for free. By the mean value property, it's sufficient to get $L^1$ convergence on compact subsets, so we might try to show there's a dominating function, or uniform integrability. And if I'm not mistaken, $\mathcal{E}(\mathbb{R})$ is a Frechet space, so we have the uniform boundedness principle available, which seems like it ought to help. | |
| Sep 17, 2018 at 9:00 | review | First posts | |||
| Sep 17, 2018 at 9:15 | |||||
| Sep 17, 2018 at 8:56 | history | asked | Giulia S-A. | CC BY-SA 4.0 |