Beurling-Lax representations using classical Lie groups with many applications. IV. GL(n,R), \(U^ *(2n)\), SL(n,\({\mathbb{C}})\), and a solvable group

DOI10.1016/0022-1236(86)90088-1zbMath0614.47003OpenAlexW1985136466MaRDI QIDQ1820377

J. William Helton, Joseph A. Ball

Publication date: 1986

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(86)90088-1

zbMATH Keywords

Lie groupBeurling-Lax theoremfull range simply invariant subspacenon full range invariant subspacesstabilizing compensators for a linear systemsymmetrized Wiener-Hopf factorization problemsYoula-Jabr-Bongiorno parametrization

Mathematics Subject Classification ID

Algebraic methods (93B25) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Invariant subspaces of linear operators (47A15) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items (4)

Shift invariant subspaces, factorization, and interpolation for matrices. I. The canonical case ⋮ Null-pole subspaces of nonregular rational matrix functions ⋮ The four-block Adamjan-Arov-Krein problem ⋮ An indefinite range inclusion theorem for triplets of bounded linear operators on a Hilbert space

Cites Work

• Minimal factorization of matrix and operator functions
• Algebraic and topological aspects of the regulator problem for lumped linear systems
• Factorization results related to shifts in an indefinite metric
• Feedback, minimax sensitivity, and optimal robustness
• Beurling-Lax Representations Using Classical Lie Groups with Many Applications III: Groups Preserving Two Bilinear Forms
• Feedback system design: The fractional representation approach to analysis and synthesis
• Modern Wiener-Hopf design of optimal controllers--Part II: The multivariable case
• On the Corona Theorem and its Application to Spectral Problems in Hilbert Space
• The factorization problem for nonnegative operator valued functions
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