000			03092nam a22004098i 4500
001			CR9781108751292
003			UkCbUP
005			20200416205231.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			181210s2020||||enk o ||1 0|eng|d
020			_a9781108751292 (ebook)
020			_z9781108485449 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA329 _b.A384 2020
082	0	0	_a515/.724 _223
100	1		_aAgler, Jim, _eauthor.
245	1	0	_aOperator analysis : _bHilbert Space Methods in complex analysis / _cJim Agler, John Edward McCarthy, Nicholas Young.
264		1	_aCambridge : _bCambridge University Press, _c2020.
300			_a1 online resource (xv, 375 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v219
500			_aTitle from publisher's bibliographic system (viewed on 06 Mar 2020).
505	0		_aThe origins of operator-theoretic approaches to function theory -- Operator analysis on D : model formulas, lurking isometries, and positivity arguments -- Further development of models on the disc -- Operator analysis on D2 -- Carathéodory-Julia theory on the disc and the bidisc -- Herglotz and Nevanlinna representations in several variables -- Model theory on the symmetrized bidisc -- Spectral sets : three case studies -- Calcular norms -- Operator monotone functions -- Motivation for non-commutative functions -- Basic properties of non-commutative functions -- Montel theorems -- Free holomorphic functions -- The implicit function theorem -- Noncommutative functional calculus.
520			_aThis book shows how operator theory interacts with function theory in one and several variables. The authors develop the theory in detail, leading the reader to the cutting edge of contemporary research. It starts with a treatment of the theory of bounded holomorphic functions on the unit disc. Model theory and the network realization formula are used to solve Nevanlinna-Pick interpolation problems, and the same techniques are shown to work on the bidisc, the symmetrized bidisc, and other domains. The techniques are powerful enough to prove the Julia-Carathéodory theorem on the bidisc, Lempert's theorem on invariant metrics in convex domains, the Oka extension theorem, and to generalize Loewner's matrix monotonicity results to several variables. In Part II, the book gives an introduction to non-commutative function theory, and shows how model theory and the network realization formula can be used to understand functions of non-commuting matrices.
650		0	_aOperator theory.
650		0	_aHolomorphic functions.
650		0	_aGeometric function theory.
650		0	_aHilbert space.
700	1		_aMcCarthy, John E. _q(John Edward), _d1964- _eauthor.
700	1		_aYoung, Nicholas, _eauthor.
776	0	8	_iPrint version: _z9781108485449
830		0	_aCambridge tracts in mathematics ; _v219.
856	4	0	_uhttps://doi.org/10.1017/9781108751292
999			_c529032 _d529030