Beurling-Lax representations using classical Lie groups with many applications. II: \(\mathrm{GL}(n,\mathbb C)\) and Wiener-Hopf factorization

DOI10.1007/BF01208379zbMath0539.47010WikidataQ115393906 ScholiaQ115393906MaRDI QIDQ793957

J. William Helton, Joseph A. Ball

Publication date: 1984

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

zbMATH Keywords

Wiener-Hopf factorizationanalytic matrix functionsinner-outer factorizationwandering subspaceBeurling-Lax-Helson-Halmos theoremfull range simply invariant subspaces

Mathematics Subject Classification ID

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 (12)

Shift invariant subspaces, factorization, and interpolation for matrices. I. The canonical case ⋮ Local inverse spectral problems for rational matrix functions ⋮ On normal solvability of the Riemann problem with singular coefficient ⋮ Commuting operators over Pontryagin spaces with applications to system theory ⋮ 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 ⋮ On symmetric factorizations of rational matrix functions ⋮ Global inverse spectral problems for rational matrix functions ⋮ An indefinite range inclusion theorem for triplets of bounded linear operators on a Hilbert space ⋮ Nevanlinna-Pick Interpolation via Graph Spaces and Kreĭn-space Geometry: A Survey ⋮ Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions: Parametrization of the set of all solutions

Cites Work

• Factorization results related to shifts in an indefinite metric
• Shifts on Hilbert spaces.
• Beurling-Lax Representations Using Classical Lie Groups with Many Applications III: Groups Preserving Two Bilinear Forms
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