Fritz Gesztesy, Yuri Latushkin, Marius Mitrea, and Maxim Zinchenko
Non-self-adjoint operators, Infinite Determinants, and some Applications
(141K, LaTeX)

ABSTRACT.  We study various spectral theoretic aspects of non-self-adjoint operators.
Specifically, we consider a class of factorable non-self-adjoint
perturbations of a given unperturbed non-self-adjoint operator and provide
an in-depth study of a variant of the  Birman-Schwinger principle as well
as local and global Weinstein-Aronszajn formulas.
Our applications include a study of suitably symmetrized (modified)
perturbation determinants of Schr\"odinger operators in dimensions
n=1,2,3 and their connection with Krein's spectral shift function
in two- and three-dimensional scattering theory. Moreover, we study
an appropriate multi-dimensional analog of the celebrated formula by Jost
and Pais that identifies Jost functions with suitable Fredholm
(perturbation) determinants and hence reduces the latter to simple
Wronski determinants.