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

2015/08/31 by Alexander Sakhnovich · 2 citations
Mathematics · #math.SP #math.CA #math.OC #msc:15A24 #msc:34A55 #msc:34B20 #msc:34D20 #msc:93B20

paper · pdf · doi:10.7153/oam-10-56

published as Operators and Matrices, Volume 10, Number 4, December 2016 · The paper is dedicated to the memory of Leiba Rodman and his results on Riccatti equations are actively used in the proof of stability. The procedure to solve inverse problem, considered in the paper, is based on the article arXiv:1105.2013

arxiv created 2015/08/31 · arxiv updated 2018/03/20

Abstract

A procedure to recover explicitly self-adjoint matrix Dirac systems on semi-axis (with both discrete and continuous components of spectrum) from rational Weyl functions is considered. Its stability is proved. GBDT version of Baecklund-Darboux transformation and various important results on Riccati equations are used for this purpose.

Cited by

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

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