= Mollifier regularization for contour recovery of support
{title2=$F_\varepsilon(z)=F(z)\widehat\rho(\varepsilon z)$}
For an <entire function> of polynomial growth and exponential type $H_K$, multiply it by $\widehat\rho(\varepsilon z)$ with a unit-mass <mollifier>. The product becomes rapidly decreasing in real frequency, so its inverse <Fourier transform> has an absolutely convergent contour integral. Shifting in a separating direction forces that smooth inverse to vanish outside $K+\varepsilon\overline B_1$. Letting $\varepsilon$ tend to zero recovers a <distribution> supported in $K$.
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