Let $$\Phi(x) = \int_{\mathbf{R}^n} e^{-|y|^n +i (x,y)} dy.$$ Is $\Phi$ positive everywhere in $\mathbf{R}^n$?
Could someone helps me answer this question or gives a reference for it? Thanks.
Is the Fourier transform of $e^{-|x|^n}$ positive?
nguyen0610
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