Spectral enclosures for non-self-adjoint discrete Schrödinger operators

Abstract

We study location of eigenvalues of one-dimensional discrete Schrödinger 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.