Lieb-Thirring and Jensen sums for non-self-adjoint Schrödinger operators on the half-line. (English) Zbl 1539.34091
Summary: We prove upper and lower bounds for sums of eigenvalues of Lieb-Thirring type for non-self-adjoint Schrödinger operators on the half-line. The upper bounds are established for general classes of integrable potentials and are shown to be optimal in various senses by proving the lower bounds for specific potentials. We consider sums that correspond to both the critical and non-critical cases.
MSC:
| 34L15 | Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
Keywords:
non-self-adjoint Schrödinger operators; discrete spectrum; Jost solutions; Lieb-Thirring type inequality; dissipative barrier potentialsReferences:
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