Sabine Bögli: On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schroedinger operators

Abstract

In the first part of this talk I will give an introduction to spectral theory of Schroedinger operators and their discrete analogues, the Jacobi operators. Lieb-Thirring inequalities give estimates on the discrete eigenvalues and their accumulation rate to the essential spectrum. Such information is useful in quantum mechanics, but the estimates are well understood only in the self-adjoint setting. In the second part of the talk I will present recent results concerning possible extensions of the Lieb-Thirring inequalities to the non-self-adjoint setting (based on joint work with Frantisek Stampach).