Recovery of the Dirac system from the rectangular Weyl matrix function

2011/06/07 by B. Fritzsche, B Fritzsche, B Kirstein +5 · 1 citation
Mathematics · Physics and Astronomy · #Dirac (video compression format) #Holomorphic and Operator Theory #Inverse #Inverse problem #Matrix (chemical analysis) #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #Type (biology) #Uniqueness #Weyl transformation #math.CA #math.FA #math.SP #msc:34B20 #msc:34L40

paper · pdf · doi:10.1088/0266-5611/28/1/015010

published as Inverse Problems 28 (2012), 015010, 18pp

arxiv created 2011/06/07 · openalex publication_date 2011/12/28 · arxiv updated 2015/05/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Weyl theory for Dirac systems with rectangular matrix potentials is non-classical. The corresponding Weyl functions are rectangular matrix functions. Furthermore, they are non-expansive in the upper semi-plane. Inverse problems are studied for such Weyl functions, and some results are new even for the square Weyl functions. High-energy asymptotics of Weyl functions and Borg–Marchenko-type uniqueness results are derived too.

Citations

• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

Cited by

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

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