Krein systems and canonical systems on a finite interval: accelerants with a jump discontinuity at the origin and continuous potentials

Details Krein systems and canonical systems on a finite interval: accelerants with a jump discontinuity at the origin and continuous potentials Krein systems and canonical systems on a finite interval: accelerants with a jump discontinuity at the origin and continuous potentials

2009-12-22

arxiv.org/abs/0912.4444v1

Integral Equations Operator Theory 68 (2010) 115-150

Mathematics

Classical Analysis and ODEs

Scientific paper

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 [1] dealing with the direct problem for Krein systems.

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