Timeline for Completeness of exponentials $\mathcal{E} = \{ e^{ist} : s \in \mathbb{R} \}$ in $L^p(\mu)$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 9, 2019 at 3:32 | comment | added | Nate Eldredge | As to this answer: Yes, certainly that works. And this is in fact the essential argument in the usual proof that the Fourier transform is injective, just without saying the words "Fourier transform". | |
| Dec 9, 2019 at 3:09 | comment | added | Nate Eldredge | @LSpice: Every finite Borel measure on $\mathbb{R}$ (or any Polish space) is Radon, which is all the regularity you need. | |
| Dec 9, 2019 at 0:31 | comment | added | LSpice | Density of continuous functions in $\operatorname L^p$ probably requires some hypothesis on the measure—regularity?—not just that it is finite and positive, right? | |
| Dec 8, 2019 at 20:35 | review | First posts | |||
| Dec 8, 2019 at 20:46 | |||||
| Dec 8, 2019 at 20:30 | history | answered | telemaco | CC BY-SA 4.0 |