Is the Fourier transform of the function
$$ f(\xi) = e^{-t|\xi|^{2m}}$$
positive for $t>0$ and $m \in \mathbb{N}\_0$?



Positivity of certain Fourier transform
it is positive for $m=1$, but not for $m=2$, see this Mathematica output:


![](https://ilorentz.org/beenakker/MO/fouriertransform.png)


