2005/11/04 by S. Kupin, Franz Peherstorfer, Kupin, S. +7
Mathematics · Physics and Astronomy · #34L25 #34L40 #42C05 #81U40 #FOS: Mathematics #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:34L25 #msc:34L40 #msc:42C05 #msc:81U40
paper · pdf · doi:10.48550/arxiv.math-ph/0511016
33 pages; a preliminary version
arxiv created 2005/11/04 · openalex publication_date 2005/11/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An original approach to the inverse scattering for Jacobi matrices was suggested in a recent paper by Volberg-Yuditskii. The authors considered quite sophisticated spectral sets (including Cantor sets of positive Lebesgue measure), however they did not take into account the mass point spectrum. This paper follows similar lines for the continuous setting with an absolutely continuous spectrum on the half-axis and a pure point spectrum on the negative half-axis satisfying the Blaschke condition. This leads us to the solution of the inverse scattering problem for a class of canonical systems that generalizes the case of Sturm-Liouville (Schrödinger) operator.