Evans functions, jost functions, and fredholm determinants

• Published in: Archive for rational mechanics and analysis Vol. 186; no. 3; pp. 361 - 421
• Main Authors: GESZTESY, Fritz, LATUSHKIN, Yuri, MAKAROV, Konstantin A
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01-12-2007; Berlin Springer Nature B.V; New York, NY
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; Numerical approximation and analysis; Ordinary and partial differential equations, boundary value problems; Physics; Studies; Operator equation; Integral operator; Generalized solution
• ISSN: 0003-9527; 1432-0673
• DOI: 10.1007/s00205-007-0071-7

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.[PUBLICATION ABSTRACT]