An inverse problem for the matrix Schrödinger equation

DOI10.1006/JMAA.2001.7792zbMath1003.34011OpenAlexW2089717771MaRDI QIDQ1599114

R. Smith

Publication date: 12 January 2003

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2001.7792

zbMATH Keywords

uniqueness theoreminverse Sturm-Liouville problemmatrix potential

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Sturm-Liouville theory (34B24) General theory of ordinary differential operators (47E05) Inverse problems involving ordinary differential equations (34A55)

Related Items (21)

Vector least-squares solutions for coupled singular matrix equations ⋮ Weyl-Titchmarsh functions of vector-valued Sturm-Liouville operators on the unit interval ⋮ Parametrization of the isospectral set for the vector-valued Sturm-Liouville problem ⋮ Uniqueness of the potential function for the vectorial Sturm-Liouville equation on a finite interval ⋮ Spectral properties of non-selfadjoint Sturm-Liouville operator with operator coefficient ⋮ Inverse problems for matrix Sturm-Liouville operators ⋮ Necessary and sufficient conditions for the solvability of the inverse problem for the matrix Sturm-Liouville operator ⋮ Spectral properties of the second order difference equation with selfadjoint operator coefficients ⋮ Stability of the inverse scattering problem for the self‐adjoint matrix Schrödinger operator on the half line ⋮ Inverse problem solution and spectral data characterization for the matrix Sturm-Liouville operator with singular potential ⋮ Spectral properties of non-selfadjoint Sturm-Liouville operator equation on the real axis ⋮ Borg-type theorems for high-order equations with matrix coefficients ⋮ On a fundamental system of solutions of the matrix Schrödinger equation with a polynomial energy-dependent potential ⋮ A spectral transform for the matrix Hill's equation ⋮ Principal functions of non-selfadjoint matrix Sturm-Liouville equations ⋮ Non-selfadjoint matrix Sturm-Liouville operators with spectral singularities ⋮ An inverse problem for the non-selfadjoint matrix Sturm–Liouville equation on the half-line ⋮ THE SPECTRUM OF QUADRATIC EIGENPARAMETER-DEPENDENT NON-SELFADJOINT MATRIX STURM-LIOUVILLE OPERATORS ⋮ Direct and inverse problems for the matrix Sturm-Liouville operator with general self-adjoint boundary conditions ⋮ Constructive solution of the inverse spectral problem for the matrix Sturm–Liouville operator ⋮ Stability of a coefficient inverse problem for the discrete Schrödinger equation and a convergence result

Cites Work

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• Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
• Eigenvalue estimates and trace formulas for the matrix Hill's equation
• Perturbation theory for linear operators.
• Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
• On the Extension of Inverse Scattering Method
• Compactness of Floquet isospectral sets for the matrix Hill's equation
• Large Eigenvalues and Trace Formulas for Matrix Sturm--Liouville Problems
• The Borg theorem for the vectorial Hill's equation

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