Krein Systems and Canonical Systems on a Finite Interval: Accelerants with a Jump Discontinuity at the Origin and Continuous Potentials

This paper is devoted to connections between accelerants and potentials of Krein systems and of canonical systems of Dirac type, both on a finite interval. It is shown that a continuous potential is always generated by an accelerant, provided the latter is continuous with a possible jump discontinuity at the origin. Moreover, the generating accelerant is uniquely determined by the potential. The results are illustrated on pseudo-exponential potentials. The paper is a continuation of the earlier paper of the authors (Alpay et al. in Modern Analysis and Applications. The Mark Krein Centenary Conference, vol. 2, pp. 19–36, OT 191. Birkhäuser, Basel, 2009) dealing with the direct problem for Krein systems.