Spectral problems for generalized Jacobi matrices

DOI10.1016/j.laa.2003.11.003zbMath1053.15018OpenAlexW1967184917MaRDI QIDQ1826811

Vladimir A. Derkach, Maxim Derevyagin

Publication date: 6 August 2004

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2003.11.003

zbMATH Keywords

convergenceinverse spectral problemSchur algorithmcontinued fractionJacobi matrixPadé approximantPontryagin spaceStone's theoremHamburger series\(m-\)function

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Inverse problems in linear algebra (15A29) Hermitian, skew-Hermitian, and related matrices (15B57) Padé approximation (41A21) Linear operator methods in interpolation, moment and extension problems (47A57) Moment problems and interpolation problems in the complex plane (30E05) Continued fractions; complex-analytic aspects (30B70) Linear operators on spaces with an indefinite metric (47B50) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (19)

Darboux transformation with parameter of generalized Jacobi matrices ⋮ Boundary Triplets, Weyl Functions, and the Kreĭn Formula ⋮ Borg-type theorems for generalized Jacobi matrices ⋮ Non-self-adjoint Jacobi matrices with a rank-one imaginary part ⋮ On the relation between Darboux transformations and polynomial mappings ⋮ An operator approach to the indefinite Stieltjes moment problem ⋮ DEK-type orthogonal polynomials and a modification of the Christoffel formula ⋮ Jacobi matrices generated by ratios of hypergeometric functions ⋮ On the convergence of Padé approximations for generalized Nevanlinna functions ⋮ Jacobi-type block matrices corresponding to the two-dimensional moment problem: polynomials of the second kind and Weyl function ⋮ A theorem of Joseph-Alfred Serret and its relation to perfect quantum state transfer ⋮ On Szegő's theorem for a nonclassical case ⋮ Asymptotics for polynomials orthogonal in an indefinite metric ⋮ Generalized Jacobi operators in Krein spaces ⋮ Shifted Darboux transformations of the generalized Jacobi matrices. I ⋮ Darboux transformations of Jacobi matrices and Padé approximation ⋮ Inverse problems for periodic generalized Jacobi matrices ⋮ Regularization of the indefinite Stieltjes moment problem ⋮ Truncations of a class of pseudo-Hermitian tridiagonal matrices

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