Colloquium header

The Krein-Lifshitz spectral shift function: its basic properties and some of its applications

4:00 pm Thursday, March 27, 2014
Fritz Gesztesy (University of Missouri)

We will describe the basic properties of the Krein-Lifshitz spectral shift function associated with a pair of self-adjoint operators and try to illustrate why it represents a powerful tool in spectral and scattering theory. To make this talk accessible, we will start with the simple case of a pair of self-adjoint matrices and then discuss the extension to general self-adjoint operators in a Hilbert space via finite-rank approximations of trace class operators. Concrete applications to spectral and scattering theory, and if time permits, also to aspects of index theory, will be provided.

Return to Colloquium page