Timeline for Is there a function that is not absolutely integrable in [−π,π] so that its Fourier Series Exists?
Current License: CC BY-SA 4.0
5 events
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| Jun 23, 2020 at 9:35 | comment | added | Bazin | @Dieter Kadelka I tried to answer the question which was "Can we define the Fourier transform on a larger set than $L^1$?". The distributional framework with temperate distribution is providing a very large space on which the Fourier transform makes sense. | |
| Jun 23, 2020 at 9:32 | comment | added | Bazin | @PhoemueX Periodic functions are defined everywhere and a classical way to obtain the classical expansion in Fourier series for a periodic distribution is to use the Fourier inversion formula above on the real line. | |
| Jun 23, 2020 at 4:56 | comment | added | PhoemueX | The OP is working on the torus $[-\pi,\pi]$, not on the whole real line. | |
| Jun 22, 2020 at 22:56 | comment | added | Dieter Kadelka | Yes, of course you can extend the domain of definition and get the above mentioned results. But I think a beginner (?) is misguided by not answering the original question. | |
| Jun 22, 2020 at 22:43 | history | answered | Bazin | CC BY-SA 4.0 |