SPECTRAL AND THRESHOLD ANALYSIS OF THE LAPLACIAN WITH NON-LOCAL POTENTIAL IN FOUR-DIMENSIONAL LATTICE
Keywords:
Discrete Schrödinger operators, essential spectrum, threshold resonance, eigenvalues, latticeAbstract
Eigenvalue behaviour of a family of discrete Schrödinger operators depending on parameter is studied on the three-dimensional lattice . The non-local potential is described by the Kronecker delta function and the shift operator. The characteristics of the Fredholm determinant at values of below the essential spectrum and their dependence on the parameters are studied. We also show that the essential spectrum absorbs the threshold eigenvalue and threshold resonance
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