On the number of eigenvalues of the discrete one-dimensional Dirac operator with a complex potential

Abstract

In this paper we define a one-dimensional discrete Dirac operator on $${\mathbb {Z}}$$ . We study the eigenvalues of the Dirac operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity. We also estimate the number of eigenvalues for the discrete Schrodinger operator with complex potential on $${\mathbb {Z}}$$ . That is we extend the result obtained by Hulko (Bull Math Sci, to appear) to the whole $${\mathbb {Z}}$$ .