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retagged: this belongs to theory of stable processes, Levy-Khintchine Thm etc.
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Abdelmalek Abdesselam
Abdelmalek Abdesselam
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added 2 characters in body
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js21
js21
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Is the Fourier transform of the function $$ f(x) = e^{-t|\xi|^{2m}}$$$$ f(\xi) = e^{-t|\xi|^{2m}}$$ positive for $t>0$ and $m \in \mathbb{N}_0$?

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

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

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Matthias Ludewig
Matthias Ludewig
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Positivity of certain Fourier transform

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