This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and repr...

Ausführliche Beschreibung

Bibliographische Detailangaben

Hauptverfasser:	Ball, Joseph A. 1947- (VerfasserIn), Bolotnikov, Vladimir 1962- (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Cambridge Cambridge University Press 2021
Schriftenreihe:	Cambridge tracts in mathematics 225
Schlagworte:	Hardy spaces Functions of complex variables
Online-Zugang:	BSB01 FHN01 Volltext
Zusammenfassung:	This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling-Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges-Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings
Beschreibung:	Title from publisher's bibliographic system (viewed on 09 Dec 2021)
Beschreibung:	1 Online-Ressource (x, 428 Seiten)
ISBN:	9781009004305
DOI:	10.1017/9781009004305