Timeline for Characterization of sums of periodic functions over the real line
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 20 at 15:26 | vote | accept | Lê Thành Dũng 'Tito' Nguyễn | ||
| Feb 6 at 16:34 | answer | added | alphacapture | timeline score: 4 | |
| Mar 8, 2023 at 18:52 | comment | added | Denis | @Gro-Tsen it is mentioned in the blog post above that it can be proven that the f and g summing to id cannot be taken measurable, but he does not provide a proof or reference. | |
| Mar 8, 2023 at 18:35 | comment | added | Lê Thành Dũng 'Tito' Nguyễn | You're right, I edited the question to clarify. | |
| Mar 8, 2023 at 18:35 | history | edited | Lê Thành Dũng 'Tito' Nguyễn | CC BY-SA 4.0 |
added 244 characters in body
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| Mar 8, 2023 at 18:08 | comment | added | Denis | @Gro-Tsen ah sorry I thought it was a classic puzzle, maybe the explanation is missing the fact that the two periodic functions are the projectors on the two subspaces of R. Adding a link to this blog post would provide better context: mathblag.wordpress.com/2013/09/01/sums-of-periodic-functions | |
| Mar 8, 2023 at 18:02 | comment | added | Gro-Tsen | @Denis Well, maybe other readers are more sharp-witted but I spent some time scratching my head wondering how the identity can be written as a finite sum of periodic functions (and it still isn't clear to me whether they can be found measurable), so I think it wouldn't do harm to clarify. | |
| Mar 8, 2023 at 17:48 | comment | added | Denis | @Gro-Tsen The example given on the identity makes it clear doesn't it ? | |
| Mar 8, 2023 at 17:45 | comment | added | Gro-Tsen | This sort of questions deserves at least a clarification that you are not demanding any sort of regularity or even measurability condition on the periodic functions in question (I guess!), so the otherwise obvious answer “the Fourier transform is supported on a finite union of $\xi\mathbb{Z}$” is thrown away. | |
| S Mar 8, 2023 at 16:13 | review | First questions | |||
| Mar 8, 2023 at 16:15 | |||||
| S Mar 8, 2023 at 16:13 | history | asked | Lê Thành Dũng 'Tito' Nguyễn | CC BY-SA 4.0 |