There are obviously real-valued functions $f$ which are bandlimited. Take, for instance, $f = \mathrm{sinc}$. Can $f$ be also non-negative at the same time?
2026-04-02 08:18:03.1775117883
Does there exist a function which is real-valued, non-negative and bandlimited?
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Take any real $L^{2}$ function $g$ which is bandlimited. Then $\hat g *\hat g$ has compact support and this is the Fourier transform of $h^{2}$ where $h(x)=g(-x)$.