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

Abstract

We characterize the set of rectangular Weyl matrix functions corresponding to Dirac systems with locally square-integrable potentials on a semi-axis and demonstrate a new way to recover the locally squareintegrable potential from the Weyl function. Important interconnections between our approach and accelerants of convolution operators are discussed as well.MSC(2010): 34B20, 34L40, 34A55, 47A48