Lieb鈥揟hirring-type sums for non-self-adjoint Schr枚dinger operators
Alexei Stepanenko: Lieb鈥揟hirring-type sums for non-self-adjoint Schr枚dinger operators
Lieb–Thirring-type sums describe the discrete eigenvalues of Schrödinger operators, in particular the rate at which they accumulate to the essential spectrum. In this talk, I will present new upper and lower bounds for such sums, in the case of Schrödinger operators on the half-line with complex potentials. In particular, our results give a detailed description of the so-called critical case. The proofs rely on expressing eigenvalues as zeros of an analytic function and applying tools from complex analysis. This is joint work with Leonid Golinskii.
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