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Operator analysis = Hilbert Space Me...

Agler, Jim.

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Operator analysis = Hilbert Space Methods in complex analysis /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Operator analysis/ Jim Agler, John Edward McCarthy, Nicholas Young.
Reminder of title:	Hilbert Space Methods in complex analysis /
Author:	Agler, Jim.
other author:	McCarthy, John E.
Published:	Cambridge :Cambridge University Press, : 2020.,
Description:	xv, 375 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 06 Mar 2020).
[NT 15003449]:	The 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 -- Caratheodory-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.
Subject:	Operator theory. -
Online resource:	https://doi.org/10.1017/9781108751292
ISBN:	9781108751292

Operator analysis = Hilbert Space Methods in complex analysis /
Agler, Jim.

Operator analysisHilbert Space Methods in complex analysis /[electronic resource] :Jim Agler, John Edward McCarthy, Nicholas Young. - Cambridge :Cambridge University Press,2020. - xv, 375 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;219. - Cambridge tracts in mathematics ;219..

Title from publisher's bibliographic system (viewed on 06 Mar 2020).

The 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 -- Caratheodory-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.

This 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-Caratheodory 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.

ISBN: 9781108751292Subjects--Topical Terms:

542531
Operator theory.

LC Class. No.: QA329 / .A384 2020

Dewey Class. No.: 515.724

Operator analysis = Hilbert Space Methods in complex analysis /
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100 1 $a Agler, Jim. $3 952118
245 1 0 $a Operator analysis $h [electronic resource] : $b Hilbert Space Methods in complex analysis / $c Jim Agler, John Edward McCarthy, Nicholas Young.
260 $a Cambridge : $b Cambridge University Press, $c 2020.
300 $a xv, 375 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 219
500 $a Title from publisher's bibliographic system (viewed on 06 Mar 2020).
505 0 $a The 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 -- Caratheodory-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 $a This 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-Caratheodory 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 $a Operator theory. $3 542531
650 0 $a Holomorphic functions. $3 700319
650 0 $a Geometric function theory. $3 606084
650 0 $a Hilbert space. $3 558371
700 1 $a McCarthy, John E. $q (John Edward), $d 1964- $3 3470594
700 1 $a Young, Nicholas. $3 922832
830 0 $a Cambridge tracts in mathematics ; $v 219. $3 3470595
856 4 0 $u https://doi.org/10.1017/9781108751292