Inverse spectral theory of finite Jacobi matrices

DOI10.1090/S0002-9947-02-03078-7zbMath1019.47029MaRDI QIDQ3151251

Peter C. Gibson

Publication date: 7 October 2002

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

orthogonal polynomialsJacobi matricesGreen functionsingular solutionsprobability distributionsTitchmarsh-Weyl \(m\)-functionexplicit formulasinverse spectral theoryfactorization of the inverse problemparametrization of the fibres

Mathematics Subject Classification ID

Inverse problems in linear algebra (15A29) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36) Inverse problems for functional-differential equations (34K29)

Related Items (2)

Non-self-adjoint Jacobi matrices with a rank-one imaginary part ⋮ A note on representations for the inverses of tridiagonal matrices

Cites Work

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• The numerically stable reconstruction of a Jacobi matrix from spectral data
• The classical moment problem as a self-adjoint finite difference operator
• Reflections on the almost Mathieu operator
• \(m\)-functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices
• A survey of matrix inverse eigenvalue problems
• Improper filtrations for C*-algebras: spectra of unilateral tridiagonal operators

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