Mathematical Physics Seminar
Wednesday, June 1, 2016
12:00pm to 1:00pmAdd to Cal
Lieb-Thirring bounds for infinite gap Jacobi matrices
Jacob Christiansen, Mathematics, Lund Univeristy,
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.