Spectral Enclosures for Non-self-adjoint Discrete Schrödinger Operators

Abstract

We study location of eigenvalues of one-dimensional discrete Schrodinger operators with complex $$\ell ^{p}$$-potentials for $$1\le p\le \infty $$. In the case of $$\ell ^{1}$$-potentials, the derived bound is shown to be optimal. For $$p>1$$, two different spectral bounds are obtained. The method relies on the Birman–Schwinger principle and various techniques for estimations of the norm of the Birman–Schwinger operator.