Skew-Self-Adjoint Dirac System with a Rectangular Matrix Potential: Weyl Theory, Direct and Inverse Problems

Skew-Self-Adjoint Dirac System with a Rectangular Matrix Potential: Weyl Theory, Direct and Inverse Problems

A non-classical Weyl theory is developed for skew-self-adjoint Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and direct and inverse problems are solved. A Borg–Marchenko type uniqueness result and the evolution of the Weyl function for the correspond...

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Veröffentlicht in:Integral equations and operator theory 2012-10, Vol.74 (2), p.163-187
Hauptverfasser: Fritzsche, B., Kirstein, B., Roitberg, I. Ya, Sakhnovich, A. L.
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Mathematics
Mathematics and Statistics
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Zusammenfassung:A non-classical Weyl theory is developed for skew-self-adjoint Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and direct and inverse problems are solved. A Borg–Marchenko type uniqueness result and the evolution of the Weyl function for the corresponding focusing nonlinear Schrödinger equation are also derived.
ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-012-1997-1