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Weyl theory for Dirac systems with rectangular matrix potentials isnon-classical. The corresponding Weyl functions are rectangular matrixfunctions. Furthermore, they are non-expansive in the upper semi-plane. Inverseproblems are treated for such Weyl functions, and some results are new even forthe square Weyl functions. High energy asymptotics of Weyl functions andBorg-Marchenko type uniqueness results are derived too.

Recovery of Dirac system from the rectangular Weyl matrix function