Boundedness conditions for entire functions of exponential type interior to the hyperoctant $\mathbf R_+^n$

Let $f(z)$ be an entire function on $\mathbf C^n$ of exponential type. This article contains an investigation of when the boundedness of $f$ on a subset dense in some sense in the positive hyperoctant $\mathbf R_+^n$ implies its boundedness on interior cones in $\mathbf R_+^n$.
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