Kirsch, AndreasSchweizer, Ben2025-06-042025-06-042025-05-15http://hdl.handle.net/2003/4372310.17877/DE290R-25497We analyze periodic operators on Rn and small perturbations of these operators. The perturbation is periodic in n − 1 directions and has bounded support in the remaining direction. We show that, when the perturbation has a sign, every spectral gap for the unperturbed operator is reduced by the perturbation. We develop a general theory that can be applied to elliptic operators, to systems such as that of linear elasticity, and to Maxwell’s equations.enband gapBloch wavesperturbation of periodic operators610preprint