I have a questions about Fourier transforms of functions in general. Let $f$ be a function and $\phi$ its Fourier transform. If $f$ has fat tails, must $\phi$ then necessarily have thin tails? Conversely, if $f$ has thin (slowly decaying) tails, must $\phi$ then necessarily have fat tails?
2026-03-25 20:34:26.1774470866
Tails of function and Fourier transform
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