Krein systems and canonical systems on a finite interval: accelerants with a jump discontinuity at the origin and continious 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. © 2010 The Author(s).