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We characterize the set of rectangular Weyl matrix functions corresponding toDirac systems with locally square-integrable potentials on a semi-axis anddemonstrate a new way to recover the locally square-integrable potential fromthe Weyl function. Important interconnections between our approach andaccelerants of convolution operators are discussed as well.

operator theory

On accelerants and their analogs, and on the characterization of the  rectangular Weyl functions for Dirac systems with locally square-integrable  potentials on a semi-axis