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We make a spectral analysis of discrete Schroedinger operators on thehalf-line, subject to complex Robin-type boundary couplings and complex-valuedpotentials. First, optimal spectral enclosures are obtained for summablepotentials. Second, general smallness conditions on the potentials guaranteeinga spectral stability are established. Third, a general identity which allows togenerate optimal discrete Hardy inequalities for the discrete DirichletLaplacian on the half-line is proved.

Spectral enclosures and stability for non-self-adjoint discrete Schroedinger operators on the half-line