Spectral Properties of Schr\"odinger Operators on Perturbed Lattices
  We study the spectral properties of Schr\"{o}dinger operators on perturbed lattices. We shall prove the non-existence or the discreteness of embedded eigenvalues, the limiting absorption principle for the resolvent, construct a spectral representation, and define the S-matrix. Our theory covers the square, triangular, diamond, Kagome lattices, as well as the ladder, the graphite and the subdivision of square lattice. 
Kazunori Ando, Hiroshi Isozaki and Hisashi Morioka
math.SP math-ph math.AP math.MP