Resonance asymptotics for quantum waveguides with semitransparent multi-perforated wall

A pair of coupled quantum waveguides with a common semitransparent wall is considered. The wall has a finite number of small windows. We consider resonance states localized near each window. The presence of several windows forces one to describe their common influence differently from that of the single-window case. Using the “matching of asymptotic expansions” method, we derive formulas for resonances and resonance states.