Inverse problem for Dirac systems with locally square-summable potentials and rectangular Weyl functions

2014/01/14 by Alexander Sakhnovich, Alexander L. Sakhnovich · 1 citation
Mathematics · #Algebraic and Geometric Analysis #Dirac (video compression format) #Dirac operator #Holomorphic and Operator Theory #Inverse #Inverse problem #Linear operators #Operator (biology) #Operator theory #Similarity (geometry) #Spectral Theory in Mathematical Physics #Square (algebra) #math.CA #math.SP #msc:34A55 #msc:34B20 #msc:34L40 #msc:47A48 #msc:47G10

paper · pdf · doi:10.4171/jst/106

published as J. Spectr. Theory 5 (2015), 547-569 · Some of the main results from [16] (A. Sakhnovich, Inverse Problems 18 (2002), 331--348) and the submitted to ArXiv papers[2] and [5] (see arXiv:0912.4444 and arXiv:1106.1263) are generalized for the case of the locally square-summable potentials and rectangular Weyl functions

arxiv created 2014/01/14 · openalex publication_date 2015/08/28 · openalex created_date 2016/06/24 · arxiv updated 2016/11/03 · openalex updated_date 2026/08/05

Abstract

Inverse problem for Dirac systems with locally square summable potentials and rectangular Weyl functions is solved. For that purpose we use a new result on the linear similarity between operators from a subclass of triangular integral operators and the operator of integration.

Citations

• Krein systems and canonical systems on a finite interval: accelerants with a jump discontinuity at the origin and continuous potentials
• Recovery of the Dirac system from the rectangular Weyl matrix function

Cited by

• Evolution of Weyl functions and initial-boundary value problems