Trace formulae for Schrödinger operators with complex-valued potentials on cubic lattices

Abstract

Abstract We consider a class of Schrödinger operators with complex decaying potentials on the lattice. Using some classical results from complex analysis we obtain some trace formulae and use them to estimate zeros of the Fredholm determinant in terms of the potential.

Keywords

• Scattering
• Trace formula
• Lattice
• Complex eigenvalues
• Hardy spaces