On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders

We consider a general elliptic operator in an infinite multi-dimensional cylinder with several distant perturbations; this is obtained by “gluing” single perturbation operators H ( k ) , = 1 … n at large distances. The coefficients of each are periodic the outlets cylinder; structure these parts different can be different. point ? 0 ? R essential spectrum perturbations and assume that not spectra middle 2 ? but eigenvalue least one . Under such assumption we show possesses finitely many resonances vicinity find leading terms asymptotics for resonances, which turn out to exponentially small. also conjecture made selects only case, when produce Namely, as do expect infinitely emerge