Local inverse spectral problems for rational matrix functions

DOI10.1007/BF01195035zbMath0621.47022OpenAlexW2042292463MaRDI QIDQ1089885

André C. M. Ran, Joseph A. Ball

Publication date: 1987

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01195035

zbMATH Keywords

Nevanlinna-Pick interpolation problemcoupling matrixregular rational matrix functionstate space formulas for the linear fractional map

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56)

Related Items (16)

Coupling operators, Wedderburn-Forney spaces, and generalized inverses ⋮ Sylvester and Lyapunov equations and some interpolation problems for rational matrix functions ⋮ Regular rational matrix functions with prescribed null and pole data except at infinity ⋮ Bitangential interpolation problems for symmetric rational matrix functions ⋮ Wiener-Hopf factorization indices of rational matrix functions with respect to the unit circle in terms of realization ⋮ State space formulas for a model matching problem ⋮ Null-pole subspaces of nonregular rational matrix functions ⋮ Minimal square spectral factors ⋮ State space theory of automorphisms of rational matrix functions ⋮ On symmetric factorizations of rational matrix functions ⋮ Minimal-degree coprime factorizations of rational matrix functions ⋮ Local minimal factorizations of rational matrix functions in terms of null and pole data: Formulas for factors ⋮ On the solution of the minimal rational interpolation problem ⋮ Vandermonde and resultant matrices: An abstract approach ⋮ A rank criterion for the order of a pole of a matrix function ⋮ Degenerate interpolation problems for Nevanlinna pairs

Cites Work

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• Beurling-Lax representations using classical Lie groups with many applications. II: \(\mathrm{GL}(n,\mathbb C)\) and Wiener-Hopf factorization
• Spectral analysis of regular matrix polynomials
• Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions: Parametrization of the set of all solutions
• Interpolation and local data for meromorphic matrix and operator functions
• An operator-theoretic approach to theorems of the Pick-Nevanlinna and Loewner types. I
• Analytic matrix functions with prescribed local data
• Rational matrix and operator functions with prescribed singularities
• Beurling-Lax Representations Using Classical Lie Groups with Many Applications III: Groups Preserving Two Bilinear Forms
• Generalized Interpolation in H ∞

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