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3:00 pm Monday, September 8, 2008 CAAM/Math Joint Colloquium: Variations on a Theme of Jost and Paisby
Fritz Gesztesy (University of Missouri) in Duncan Hall 1064- 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 Schr\"odinger operator on a half-line to a simple Wronski determinant of appropriate distributional solutions of the underlying Schr\"odinger 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.
Submitted by damanik@rice.edu |