The inverse approach to Dirac-type systems based on the A-function concept

Generalised canonical systems related to matrix string equations: corresponding structured operators and high-energy asymptotics of the Weyl functions

“…Related results one can find in [16] and in [26, (32)] for self-adjoint Dirac systems, and in [27, p. 319] for skew-self-adjoint Dirac systems, with various interesting developments in [3,4,10,28].…”

“…Krein. See further developments, discussions and references in [10,21,28,32,[36][37][38]. The case of S satisfying operator identity (or equation) (3.2), where A is given in (2.10), that is,…”

Characterization of the periodic and antiperiodic spectra of non-self-adjoint Dirac operators

“…Also inverse theory was intensively developed for Dirac-type operators on the axis and semiaxis by many authors. New inverse approach to such differential systems on the semiaxis based on A-function concept was recently considered in [7].…”

On a class of canonical systems corresponding to matrix string equations: general-type and explicit fundamental solutions and Weyl--Titchmarsh theory

“…Well-known Dirac (or Dirac-type) systems are equivalent to a special subclass of canonical systems (see [15,17,43,45,50] and references therein). The Hamiltonians corresponding to Dirac systems (after we switch from the representation (1.1) to the representation (1.4)), have the form…”