arXiv subjects
Publications and source records attributed to Hisashi Morioka.
We study the spectral properties of Schrödinger 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.
An analogue of Rellich's theorem is proved for discrete Laplacian on square lattice, and applied to show unique continuation property on certain domains as well as non-existence of embedded eigenvalues for discrete Schr{ö}dinger operators.
We study an inverse scattering problem for the discrete Schrödinger operator on the multi-dimensional square lattice, with compactly supported potential. We show that the potential is uniquely reconstructed from a scattering matrix for a fixed energy.