Fritz Gesztesy, Yuri Latushkin, and Konstantin A. Makarov
Evans Functions, Jost Functions, and Fredholm Determinants
(200K, LaTeX)
ABSTRACT. The principal results of this paper consist of an intrinsic definition
of the Evans function in terms of newly introduced generalized
matrix-valued Jost solutions for general first-order matrix-valued
differential equations on the real line, and a proof of the fact that the
Evans function, a finite-dimensional determinant by construction,
coincides with a modified Fredholm determinant associated with a
Birman-Schwinger-type integral operator up to a nonvanishing
factor.