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

2009/12/22 by D. Alpay, I. Gohberg, M. A. Kaashoek +2 · 1 citation
Mathematics · #math.CA #math.SP #msc:34L40 #msc:47A68 #msc:47B65

paper · pdf

published as Integral Equations Operator Theory 68 (2010) 115-150

arxiv created 2009/12/22 · arxiv updated 2011/04/05

Abstract

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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• Inverse problem for Dirac systems with locally square-summable potentials and rectangular Weyl functions

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