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  dealing with the direct problem for Krein systems.
D. Alpay, I. Gohberg, M.A. Kaashoek, L. Lerer and A. Sakhnovich. Krein systems and canonical systems on a finite interval: accelerants with a jump discontinuity at the origin and continuous potentials. Integral Equations and Operator Theory, vol. 68 (issue 1), pp. 115 - 150 (2010).
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This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Integral Equations and Operator Theory, volume 68, issue 1, in 2010 following peer review. The final publication is available at Springer via DOI: 10.1007/s00020-010-1803-x