Operator identities corresponding to inverse problems

TL;DR

This paper investigates structured operators and their identities in inverse problems related to Dirac systems, highlighting classes with displacement kernels and analyzing positive, factorizable operators.

Contribution

It provides a detailed study of operator identities in inverse Dirac problems, including classes with displacement kernels and special cases of positive, factorizable operators.

Findings

Operators with displacement kernels are included in the studied class.

Special case analysis of positive and factorizable operators.

Detailed characterization of operator identities in inverse Dirac problems.

Abstract

The structured operators and corresponding operator identities, which appear in inverse problems for the self-adjoint and skew-self-adjoint Dirac systems with rectangular potentials, are studied in detail. In particular, it is shown that operators with the close to displacement kernels are included in this class. A special case of positive and factorizable operators is dealt with separately.