000			02646nam a22003857a 4500
003			IIITD
005			20260226131957.0
008			260222b |||||||| |||| 00| 0 eng d
020			_a9781316518991
040			_aIIITD
050	0	0	_aQA331 _b.B24 2021
082	0	0	_a515.9 _223 _bBAL-N
100	1		_aBall, Joseph A.
245	1	0	_aNoncommutative function-theoretic operator theory and applications _cby Joseph A. Ball and Vladimir Bolotnikov
260			_aNew York : _bCambridge Universirty Press, _c©2022
300			_ax, 428 p.; _c25 cm.
490	0		_aCambridge tracts in mathematics; _v225
504			_aIncludes bibliographical references and index.
505			_t1. Introduction
505			_t2. Formal Reproducing Kenel Hilbert Spaces
505			_t3. Contractive multipliers
505			_t4. Stein relations and observability range spaces
505			_t5. Beurling-Lax theorems based on contractive multipliers
505			_t6. Non-orthogonal Beurling-Lax representations
505			_t7. Orthogonal Beurling-Lax representations
505			_t8. Models for -hypercontractive operator tuples
505			_t9. Regular formal power series
520			_a"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 subspacesubspaces 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"--
650		0	_aHardy spaces.
650		0	_aFunctions of complex variables.
650		7	_aMATHEMATICS / Algebra / Abstract
700	1		_aBolotnikov, Vladimir
776	0	8	_iOnline version: _aBall, Joseph A., 1947- _tNoncommutative function-theoretic operator theory and applications _b1. _dNew York : Cambridge University Press, 2021 _z9781009004305 _w(DLC) 2021024661
942			_2ddc _cBK
999			_c209710 _d209710