Beurling-Lax representations using classical Lie groups with many applications. IV. GL(n,R), \(U^ *(2n)\), SL(n,\({\mathbb{C}})\), and a solvable group
type: Item
instance of: scholarly article
title: Beurling-Lax representations using classical Lie groups with many applications. IV. GL(n,R), \(U^ *(2n)\), SL(n,\({\mathbb{C}})\), and a solvable group
zbMATH Open document ID: 0614.47003
DOI: 10.1016/0022-1236(86)90088-1
author: J. William Helton
author: Joseph A. Ball
published in: Journal of Functional Analysis
publication date: 1986-01-01T00:00:00Z
review text: The Beurling-Lax theorem implies that any full range simply invariant subspace M of \(L^ 2_ n\) (square integrable vector valued functions on the unit circle) can be represented as \(\theta H^ 2_ n\) where \(\theta (e^{it})\) is unitary for almost all t. The authors here continue their study of characterizing subspaces M for which the Lie group U(n) of unitary matrices can be replaced by the other of the classical Lie groups. Applications include new types of symmetrized Wiener-Hopf factorization problems. The paper also includes a study of representations of certain types of non full range invariant subspaces; as an application there is obtained a geometric (module-theoretic) derivation of the Youla-Jabr-Bongiorno parametrization of all stabilizing compensators for a linear system. [For part III see Am. J. Math. 108, 95- 174 (1986; Zbl 0601.47015).]
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 22E45
Mathematics Subject Classification ID: 47A56
zbMATH DE Number: 3994331
zbMATH Keywords: Beurling-Lax theorem
zbMATH Keywords: full range simply invariant subspace
zbMATH Keywords: Lie group
zbMATH Keywords: symmetrized Wiener-Hopf factorization problems
zbMATH Keywords: non full range invariant subspaces
zbMATH Keywords: Youla-Jabr-Bongiorno parametrization
zbMATH Keywords: stabilizing compensators for a linear system
MaRDI profile type: Publication
full work available at URL: 0022-1236(86)90088-1
OpenAlex ID: W1985136466
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description: scientific article; zbMATH DE number 3994331