Beurling-Lax Representations Using Classical Lie Groups with Many Applications III: Groups Preserving Two Bilinear Forms

DOI10.2307/2374470zbMath0601.47015OpenAlexW2318247238WikidataQ115228813 ScholiaQ115228813MaRDI QIDQ3736378

J. William Helton, Joseph A. Ball

Publication date: 1986

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2374470

zbMATH Keywords

Hardy spacerepresentationLie groupbroadband impedance matchingBeurling-Lax invariant subspace representationsBeurling-Lax-Halmos-Helson theorembilateral shift operatorDarlington embeddinggeometry of Krein spacesinner-outer and spectral factorizationmatrix Nevanlinna-Pick interpolation problempreserving a Hermitian form and a complex symmetric form simultaneouslysimply invariant subspace

Mathematics Subject Classification ID

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 (15)

Shift invariant subspaces, factorization, and interpolation for matrices. I. The canonical case ⋮ Local inverse spectral problems for rational matrix functions ⋮ Analytic system problems and \(J\)-lossless coprime factorization for infinite-dimensional linear systems ⋮ An alternative solution to the \(H_{\infty}\)-optimal control problem ⋮ Parametric interpolation, H ^∞-control and model reduction ⋮ Bitangential interpolation problems for symmetric rational matrix functions ⋮ The Beurling-Lax-Halmos theorem for infinite multiplicity ⋮ Null-pole subspaces of nonregular rational matrix functions ⋮ Pairs of shift invariant subspaces of matrices and noncanonical factorization ⋮ Hankel norm approximation of real symmetric rational matrix functions ⋮ Nehari problems and equalizing vectors for infinite-dimensional systems ⋮ Beurling-Lax representations using classical Lie groups with many applications. IV. GL(n,R), \(U^ *(2n)\), SL(n,\({\mathbb{C}})\), and a solvable group ⋮ An indefinite range inclusion theorem for triplets of bounded linear operators on a Hilbert space ⋮ Beurling-Lax representations using classical Lie groups with many applications. II: \(\mathrm{GL}(n,\mathbb C)\) and Wiener-Hopf factorization ⋮ Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions: Parametrization of the set of all solutions

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