| Contents |
| We talk about the spectral properties of Schroedinger operators on perturbed lattices. We shall prove non-existence of embedded eigenvalues, limiting absorption principle for the resolvent, construct spectral representation, and define the S-matrix. Based on these forward problem results, we will discuss the inverse scattering, i.e. reconstruction of the potential term or the perturbation of the local part of the lattice from the knowledge of the S-matrix of one fixed energy. Our theory covers square, triangular, hexagonal, Kagome, diamond, subdivision lattices, as well as ladder and graphite. |
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