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Archive for Rational Mechanics and Analysis

, Volume 186, Issue 3, pp 361–421 | Cite as

Evans Functions, Jost Functions, and Fredholm Determinants

  • Fritz GesztesyEmail author
  • Yuri Latushkin
  • Konstantin A. Makarov
Article
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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 an explicitly computable nonvanishing factor.

Keywords

Lyapunov Exponent Evans Function Integral Kernel Volterra Integral Equation Exponential Dichotomy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Fritz Gesztesy
    • 1
    Email author
  • Yuri Latushkin
    • 1
  • Konstantin A. Makarov
    • 1
  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA

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