Timeline for $T$ is tempered distribution that is harmonic,then $T$ is polynomial
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2020 at 6:35 | comment | added | Denis Serre | @Lamda8. I mean the fact that if $\ker f\subset\ker g$, where $f$ targets a finite-dimensional space, then there exists an $h$ such that $g=h\circ f$ (here everything is linear). | |
| Apr 12, 2020 at 23:34 | comment | added | Lamda8 | Maybe a stupid question but how does the "by elemetary linear algebra" works? | |
| Oct 14, 2019 at 15:33 | comment | added | Denis Serre | @Salamo. Just because on every open domain of ${\mathbb R}^n\setminus\{0\}$, $|x|^2$ is uniformly positive and therefore invertible. | |
| Oct 14, 2019 at 15:13 | comment | added | Salamo | Maybe a stupid question. But why does $\lvert\xi\rvert^2\hat{T}=0$ imply that the support of $\hat{T}$ is $\{0\}$? | |
| Aug 9, 2017 at 17:17 | vote | accept | Rahul Raju Pattar | ||
| Dec 7, 2016 at 15:41 | comment | added | Denis Serre | @ მამუკა ჯიბლაძე . On every compact subset, a distribution is of finite order, by definition. | |
| Dec 7, 2016 at 15:31 | comment | added | მამუკა ჯიბლაძე | @Bazin Is finiteness obvious? Theoretically there could exist some infinite linear combinations of derivatives at zero which converge for every $\phi$... | |
| Dec 7, 2016 at 13:30 | comment | added | Bazin | Once you know that the support of $\hat T$ is $\{0\}$, you are done: in fact, $\hat T$ is a (finite) linear combination of derivatives of the Dirac mass at 0, whose inverse Fourier transforms are monomials. | |
| Dec 7, 2016 at 12:11 | history | edited | Denis Serre | CC BY-SA 3.0 |
added 200 characters in body
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| Dec 6, 2016 at 14:19 | history | answered | Denis Serre | CC BY-SA 3.0 |