Timeline for What are the spaces for which the Fourier transform is an automorphism? [closed]
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 11, 2016 at 10:25 | history | closed |
Yemon Choi Stefan Waldmann Wolfgang Alex Degtyarev Stefan Kohl♦ |
Needs more focus | |
| Mar 11, 2016 at 7:57 | answer | added | oeiras | timeline score: 3 | |
| Mar 11, 2016 at 1:44 | review | Close votes | |||
| Mar 11, 2016 at 10:25 | |||||
| Mar 11, 2016 at 1:26 | comment | added | Yemon Choi | Unfortunately, "interesting examples that I'm not aware of, not some trivial examples made from the spaces I talked about" does not seem well-defined to me. The Lebesgue-Fourier algebra is just as trivial or non-trivial as @ADe's examples, but because I named the spaces maybe it looks better. "Spaces of functions" can be very very varied and I think your question needs to say something about what kinds of function spaces you want (Lorentz spaces? Banach lattices?) rather than waiting for people to suggest things and for you to say "oh, no that's not what I meant" | |
| Mar 10, 2016 at 22:49 | comment | added | reuns | what if you write something like $S(\mathbb{R}) = P[L^2(\mathbb{R})]$ where $P[f](x) = [(f(y)e^{-\epsilon^2 y^2}) \ast (\epsilon e^{-y^2/\epsilon^2})](x)$ ? | |
| Mar 10, 2016 at 21:29 | comment | added | Héhéhé | Of course I mean interesting examples that I'm not aware of, not some trivial examples made from the spaces I talked about. Thanks for your answer about Lebesgue-Fourier algebra. | |
| Mar 10, 2016 at 20:49 | comment | added | Yemon Choi | I think @ADe's observation shows that your question is not quite well-posed, in the sense you intend. I could also mention $L^1({\bf R})\cap A({\bf R})$, sometimes known as the Lebesgue-Fourier algebra | |
| Mar 10, 2016 at 20:22 | comment | added | user1688 | Take any subspace $V$ of either of the spaces and let $F$ denote the Fourier-transform. Then it will be an automorphism on $V+F(V)+F^2(V)+F^3(V)$. | |
| Mar 10, 2016 at 20:15 | history | asked | Héhéhé | CC BY-SA 3.0 |