Timeline for Eigenvectors of the Fourier transformation
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jan 5, 2018 at 22:36 | comment | added | user90189 | Did you notice that in $\mathbb{R}^2$, the distribution $\langle T,\phi\rangle = \int \phi(x,0)\,dx+\int\phi(0,y)\,dy$ is an eigenvalue? There are other similar examples. | |
| Dec 20, 2017 at 7:17 | review | Close votes | |||
| Dec 20, 2017 at 8:45 | |||||
| Dec 20, 2017 at 7:01 | comment | added | Nemo | Possible duplicate of What are fixed points of the Fourier Transform | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| May 11, 2016 at 13:25 | history | edited | Denis Serre | CC BY-SA 3.0 |
added 6 characters in body
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| May 11, 2016 at 12:39 | comment | added | Gro-Tsen | Not claiming to answer your question, but in $L^2(\mathbb{R})$, an orthonormal basis that diagonalizes the Fourier transform is given by the Hermite functions $H_n(x)\,e^{-x^2/2}$. The closed span of those for $n$ multiple of $4$ gives a convenient description of $L^2$ functions equal to their Fourier transform. | |
| May 11, 2016 at 12:38 | comment | added | Jochen Wengenroth | The answer in your edit has almost nothing to do with Fourier transformation and uses only linearity and the periodicity. Are you really satisfied by this characterization? | |
| May 11, 2016 at 12:15 | history | edited | Bazin | CC BY-SA 3.0 |
I found the answer, thanks to your answers and to the reference: http://mathoverflow.net/questions/12045/what-are-fixed-points-of-the-fourier-transform?lq=1
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| May 10, 2016 at 17:24 | comment | added | Bazin | I am most grateful for all the answers below. However I am looking for all the tempered distributions solutions $T$ such that $\mathcal F T=T$. | |
| May 10, 2016 at 13:42 | answer | added | Alexandre Eremenko | timeline score: 9 | |
| May 10, 2016 at 13:05 | answer | added | Igor Rivin | timeline score: 10 | |
| May 10, 2016 at 13:03 | answer | added | Carlo Beenakker | timeline score: 24 | |
| May 10, 2016 at 12:47 | history | asked | Bazin | CC BY-SA 3.0 |