Timeline for Uniqueness of Fourier–Stieltjes transform for finite complex valued measures
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 8, 2023 at 14:32 | vote | accept | Boby | ||
| Jan 7, 2023 at 16:20 | comment | added | Vinícius Novelli | @Boby I mean that $\mathcal{S}(\mathbb{R}) \subset C_0(\mathbb{R})$ is dense when $C_0(\mathbb{R})$ is endowed with the Banach norm $\|f\|_{C_0(\mathbb{R})}=\sup_{\mathbb{R}}|f|$. This has a standard proof using mollifiers, see here for example. For Riesz's theorem you can check Rudin's Real and Complex Analysis, chapter 6. For this proof in particular I don't know a reference, but it's so simple that I doubt you need one. | |
| Jan 7, 2023 at 16:15 | comment | added | Boby | What do you mean 'by the density'. I couldn't follow that sentence fully. Also, do you have a good reference where I can find this proof. I want to cite something. | |
| Jan 7, 2023 at 16:09 | history | answered | Vinícius Novelli | CC BY-SA 4.0 |