Mathematical Physics Seminar

In the talk, I'll explain how to establish Lieb-Thirring bounds on the discrete eigenvalues of Jacobi matrices for Schatten class perturbations under very general assumptions. The results apply, e.g., to perturbations of reflectionless Jacobi matrices with Cantor-type essential spectrum. 

 

 As we'll see, the first step in the procedure is to obtain trace norm estimates by use of a Cauchy-type integral. The next issue is then how to estimate a variant of the m-function which has an absolute value under the integral sign. Once this is settled, the Lieb-Thirring bounds follow from a version of the Birman-Schwinger principle.

 

The talk is based on joint work with Maxim Zinchenko, UNM.