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Skew-self-adjoint discrete and continuous Dirac-type systems: inverse problems and Borg–Marchenko theorems

Alexander Sakhnovich 2006 Inverse Problems 22 2083-2101   doi: 10.1088/0266-5611/22/6/011  Help

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Alexander Sakhnovich
Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Austria
E-mail: al_sakhnov@yahoo.com

Abstract. New formulae on the inverse problem for the continuous skew-self-adjoint Dirac-type system are obtained. For the discrete skew-self-adjoint Dirac-type system the solution of a general-type inverse spectral problem is also derived in terms of the Weyl functions. The description of the Weyl functions on the interval is given. Borg–Marchenko-type uniqueness theorems are also derived for both discrete and continuous non-self-adjoint systems.

Print publication: Issue 6 (December 2006)
Received 7 January 2006, in final form 19 September 2006
Published 20 October 2006

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