Evans Functions, Jost Functions, and Fredholm Determinants

2005/11/15 by Gesztesy, Fritz, Latushkin, Yuri, Makarov, Konstantin A. · 2 citations
#34B27 #34L40 #47B10 #47G10 #Dynamical Systems (math.DS) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.math/0511372

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.

Cited by

• Resonances for the one dimensional Schrödinger operator with the matrix-valued complex square-well potential
• Numerical Fredholm determinants for matrix-valued kernels on the real line

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