Spectral enclosures and stability for non‐self‐adjoint discrete Schrödinger operators on the half‐line
David Krejčiřı́k, Ари Лаптев, František Štampach
Abstract
We make a spectral analysis of discrete Schrödinger 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.
Topics & Concepts
MathematicsDiscrete spectrumHalf lineStability (learning theory)Dirichlet distributionSchrödinger's catSpectral theoryLaplace operatorIdentity (music)Boundary (topology)Pure mathematicsType (biology)Line (geometry)Mathematical analysisBoundary value problemApplied mathematicsEigenvalues and eigenvectorsHilbert spaceGeometryQuantum mechanicsComputer scienceBiologyAcousticsMachine learningEcologyPhysicsSpectral Theory in Mathematical PhysicsNumerical methods in inverse problemsAdvanced Mathematical Modeling in Engineering