Does there exist a function which is real-valued, non-negative and bandlimited?

Question

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?

Kavi Rama Murthy · Answer

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 $h(x)=g(-x)$.

Does there exist a function which is real-valued, non-negative and bandlimited?

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