Abstract: We consider a spectral problem for the Laplace operator in a periodic waveguide ? ? ?3 perturbed by a family of ?heavy concentrated masses?; namely, ? contains small regions {???? ?? }???? of high density, which are periodically distributed along the ?? axis. Each domain ???? ?? ? ? has a diameter ??(??) and the density takes the value ????? in ???? ?? and 1 outside; ?? and ?? are positive parameters, ?? > 2, ?? ? 1. Considering a Dirichlet boundary condition, we study the band-gap structure of the essential spectrum of the corresponding operator as ?? ? 0.We provide information on the width of the first bands and find asymptotic formulas for the localization of the possible gaps.

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