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Spectral enclosures and stability for non-self-adjoint discrete Schroedinger operators on the half-line (2111.08265v1)

Published 16 Nov 2021 in math.SP, math-ph, math.CA, and math.MP

Abstract: We make a spectral analysis of discrete Schroedinger operators on the half-line, subject to complex Robin-type boundary couplings and complex-valued potentials. First, optimal spectral enclosures are obtained for summable potentials. Second, general smallness conditions on the potentials guaranteeing a spectral stability are established. Third, a general identity which allows to generate optimal discrete Hardy inequalities for the discrete Dirichlet Laplacian on the half-line is proved.

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