000			02174cam a22003258i 4500
003			OSt
005			20240529100231.0
008			191125s2019 nyu b 001 0 eng
020			_a9781108485449
040			_aNISER LIBRARY _beng _cNISER LIBRARY
041			_aEnglish
082	0	0	_a517.98 _bAGL-O
100	1		_aAgler, Jim.
245	1	0	_aOperator analysis : _bhilbert space methods in complex analysis
260			_aCambridge : _bCambridge University Press, _c2020.
300			_axv, 375p. : _billustrations ; _c24 cm.
490			_aCambridge tracts in mathematics ; _v219
504			_aIncludes bibliographical references and index.
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)
700	1		_aYoung, Nicholas.
856			_3Table of Contents _uhttps://assets.cambridge.org/97811084/85449/toc/9781108485449_toc.pdf
856			_3Excerpt _uhttps://assets.cambridge.org/97811084/85449/excerpt/9781108485449_excerpt.pdf
856			_3Reviews _uhttps://www.goodreads.com/book/show/53030565-operator-analysis#CommunityReviews
942			_cBK _2udc
999			_c34886 _d34886