Threshold of discrete Schr\"odinger operators with delta potentials on $n$-dimensional lattice

Abstract

Eigenvalue behaviors of Schr\"odinger operator defined on $n$-dimensional lattice with $n+1$ delta potentials is studied. It can be shown that lower threshold eigenvalue and lower threshold resonance are appeared for $n\geq 2$, and lower super-threshold resonance appeared for $n=1$.