Kouichi Taira - Spectral properties and resolvent estimates for discrete Schr枚dinger operators

In this talk, we introduce some results on resolvent estimates for discrete Schrödinger operators near real axis. Such operators appear as a tight-binding approximation of a model of an electron moved on the square lattice.  Spectral and scattering theory of discrete Schrödinger operators have been studied in recent years. Here, we consider discrete Schrödinger operators with l^p-potentials, in particular, anisotropic potentials. We show that the resolvents of such operators have worse behavior than the continuous one’s probably due to the lack of spherical symmetry of the lattice. Moreover, we explain applications to spectral and scattering theory.