  We prove, under certain conditions on $(\alpha,\beta)$, that each Schwartz
function $f$ such that $f(\pm n^{\alpha}) = \hat{f}(\pm n^{\beta}) = 0, \forall
n \ge 0$ must vanish identically, complementing a series of recent results
involving uncertainty principles, such as the pointwise interpolation formulas
by Radchenko and Viazovska and the Meyer-Guinnand construction of self-dual
crystaline measures.
