Skew-selfadjoint Dirac systems: stability of the procedure of explicit solving the inverse problem

2015/10/31 by B. Fritzsche, B. Kirstein, I. Ya. Roitberg +1 · 1 citation
Mathematics · #math.SP #math.CA #math.OC #msc:15A24 #msc:15A29 #msc:34A55 #msc:34B20 #msc:34D20 #msc:93B20

paper · pdf · doi:10.1016/j.laa.2017.07.034

published as Linear Algebra and its Applications, 533 (2017) 428-450 · This paper is related to the paper arXiv:1508.07954 and deals with the case of discrete and continuous skew-selfadjoint Dirac systems (instead of the continuous selfadjoint case in arXiv:1508.07954). The discrete case is added in the current version

arxiv created 2016/01/31 · arxiv updated 2018/03/20

Abstract

Procedures to recover explicitly discrete and continuous skew-selfadjoint Dirac systems on semi-axis from rational Weyl matrix functions are considered. Their stability is shown. Some new facts on asymptotics of pseudo-exponential potentials (i.e., of explicit solutions of inverse problems) are proved as well. GBDT version of Backlund-Darboux transformation, methods from system theory and results on algebraic Riccati equations are used for this purpose.

Citations

• Inverse problems for self-adjoint Dirac systems: explicit solutions and stability of the procedure

Cited by

• General-type discrete self-adjoint Dirac systems: explicit solutions of direct and inverse problems, asymptotics of Verblunsky-type coefficients and stability of solving inverse problem