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Evans functions, Jost functions, and Fredholm determinants. (English) Zbl 1134.34004

Summary: 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 an explicitly computable nonvanishing factor.

MSC:

34A30 Linear ordinary differential equations and systems
47E05 General theory of ordinary differential operators
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