Consider the Fourier transform of $\exp(-z^k)$ where $k$ is a positive integer. As the function is analytic, I expect it to
have exponential decay at infinity. Is there some known theorem giving a quantitative estimate for that decay?
(Some variant of the Paley–Wiener theorem useful for this case?)
Off course if k=2 we get (up to a constants) the same function, but I don't expect an explicit formula for other values of k.