Scale-free Hankel factorization and explicit one-dimensional plunge bounds for time-frequency localization operators

The plunge region records the spectral transition of a time-frequency localization operator. Let $A_0,B_0\subset\mathbb{R}$ be bounded measurable sets of positive measure with finite boundaries, and let $S_{cA_0,B_0}=P_{cA_0}Q_{B_0}P_{cA_0}$. We prove that, for every $c>0$ and $0<\varepsilon<1/2$,