Evans Functions, Jost Functions, and Fredholm Determinants

Details Evans Functions, Jost Functions, and Fredholm Determinants Evans Functions, Jost Functions, and Fredholm Determinants

2005-11-15

arxiv.org/abs/math/0511372v1

Mathematics

Dynamical Systems

53 pages

Scientific paper

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.

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