On spectrum and threshold analysis for discrete Schrödinger operator.

We consider a family of the discrete Schrödinger operators Hλμ, in the d (d ≥ 3)-dimensional lattice with a wide class of dispersion relation and a potential constructed by a combination of the Kronecker delta function and the shift operator, depending on two parameters. The exstence of eigenvalues, threshold eigenvalues and threshold resonances and their dependence on the parameters of the operator and dimension of the lattice are explicitly derived. [ABSTRACT FROM AUTHOR]