Greenfeld and Lev conjectured that the Cartesian product of two sets $A$ and $B$ is spectral if and only if $A$ and $B$ are spectral. We construct a counterexample to this fact using the existence of a tile that has no spectra.
Spectrality of a class of infinite convolutions on $\mathbb{R}$
Spectrality and tiling by cylindric domains
Spectrality of Infinite Convolutions in $\mathbb{R}^d$
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