Instructor: Fritz Gesztesy

Description: We intend to continue our discussion of infinite determinants and their applications in applied and mathematical physics.

In particular, we will discuss the relevance and applicability of infinite determinants in Floquet theory of periodic differential operators (Floquet discriminants, etc.), spectral and scattering theory of Schrodinger-type operators (Jost functions and their multi-dimensional analogs), linear stability theory arising in nonlinear evolution equations (Evans functions, etc.). The differential operators discussed will be ordinary and partial differential operators.

We also plan to discuss the stability of the absolutely continuous spectrum of self-adjoint operators under certain classes of Hilbert--Schmidt perturbations under additional conditions of boundary values of perturbation determinants.

If time permits, we may also introduce a new way of obtaining spectral representations for self-adjoint multi-dimensional Schrodinger operators.

Prerequisites: The current Math 9487 Mathematical Physics Seminar in the FS 2006.