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

TL;DR

This paper characterizes the set of Weyl matrix functions for Dirac systems with square-integrable potentials and introduces a novel method to recover these potentials from the Weyl functions, highlighting links to convolution operator accelerants.

Contribution

It provides a new characterization of Weyl functions for Dirac systems with locally square-integrable potentials and a method for potential recovery from these functions.

Findings

Characterization of Weyl matrix functions for the specified Dirac systems

A new method for recovering potentials from Weyl functions

Discussion of connections to convolution operator accelerants

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 square-integrable potential from the Weyl function. Important interconnections between our approach and accelerants of convolution operators are discussed as well.