Analogue of the resonance-string characterization for delta-function potentials

Establish the analogue of Theorem 1.7 for semiclassical resonances of one-dimensional Schrödinger operators with multiple delta-function potentials, namely, determine whether every sequence of resonances in the right half-plane has a subsequence asymptotic to one of the finitely many logarithmic resonance strings characterized by the corresponding parameter data.

Background

Theorem 1.7 in the paper proves, for the class $\mathcal V$, that every sequence of resonances in the right half-plane has a subsequence approaching a logarithmic curve associated with a discontinuity of $\ell_V'$. The authors compare this result with the setting studied in earlier work on semiclassical resonances for one-dimensional operators with multiple delta-function potentials.

That comparison identifies the corresponding characterization theorem as unresolved in the delta-potential setting; the paper explicitly points to Conjecture 1 of the cited work as the relevant formulation.