Colloquium

Scheduled Talk - September 8, 2008 - [ 3:00PM in DH 1064 ]

Fritz Gesztesy
Department of Mathematics
University of Missouri

"Variations on a Theme of Jost and Pais"

Abstract:
We explore the extent to which a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with the Schrödinger operator on a half-line to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrödinger equation, generalizes to higher dimensions.

In this multi-dimensional extension the half-line is replaced by an open set in R^n, with a compact, nonempty boundary satisfying certain regularity conditions. Our variant involves ratios of perturbation determinants corresponding to Dirichlet and Neumann boundary conditions on the boundary and invokes the corresponding Dirichlet-to-Neumann map.

If time permits, applications involving the Birman-Schwinger principle and eigenvalue counting functions will be discussed.

The talk will also briefly review basic elements of infinite determinants and some of their modifications.