Direct and inverse asymptotic scattering problems for Dirac--Krein systems

DOI10.1007/s10688-007-0016-9zbMath1156.47010OpenAlexW2021110034MaRDI QIDQ1002776

Harry Dym, Damir Z. Arov

Publication date: 26 February 2009

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10688-007-0016-9

zbMATH Keywords

inverse problemHilbert spaceHankel operatorToeplitz operatorWiener classNehari problemmatrix-valued functionlinear bounded operatorSchur problemasymptotic scattering matrix

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General theory of ordinary differential operators (47E05) Linear operator methods in interpolation, moment and extension problems (47A57) Scattering theory of linear operators (47A40) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (3)

The bitangential inverse spectral problem for canonical systems ⋮ Inverse scattering on the half-line for generalized ZS-AKNS system with general boundary conditions ⋮ Inverse scattering on the half-line for a first-order system with a general boundary condition

Cites Work

• Numerical solution of integral equations, fast algorithms and Krein- Sobolev equation
• Spectral theory of canonical differential systems. Method of operator identities
• On three Klein extension problems and some generalizations
• \(J\)-inner matrix functions, interpolation and inverse problems for canonical systems. V: The inverse input scattering problem for Wiener class and rational \(p\times q\) input scattering matrices
• The bitangential inverse spectral problem for canonical systems
• On Krein's differential system and its generalization
• Direct and inverse problems for differential systems connected with Dirac systems and related factorization problems
• Continuous analogs of polynomials orthogonal on the unit circle and Krein systems
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