Operator analysis : Hilbert space methods in complex analysis / Jim Agler, John Edward McCarthy, Nicholas Young.

Format:

Book

Author/Creator:

Agler, Jim, author.

McCarthy, John E. (John Edward), 1964- author.

Young, Nicholas, author.

Series:

Cambridge tracts in mathematics ; 219.

Cambridge tracts in mathematics ; 219

Language:

English

Subjects (All):

Operator theory.

Holomorphic functions.

Geometric function theory.

Hilbert space.

Physical Description:

xv, 375 pages : illustrations ; 24 cm.

Other Title:

Hilbert space methods in complex analysis

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2020.

Summary:

"The philosophy of this book is that Hilbert space geometry binds function theory and operator theory together, not only allowing each to aid the other, but creating a rich structure that can be used to discover new phenomena. There is a "three-way street" between operator theory and function theory: sometimes one uses function theory to prove operator theorems, sometimes one uses operator theory to prove function theorems, and sometimes the theories are so interwoven that one cannot even state the theorem without using the language of both operator theory and function theory"-- Preface.

Contents:

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

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.

Notes:

Includes bibliographical references (pages 361-371) and index.

Other Format:

Online version: Agler, Jim. Operator analysis.

ISBN:

9781108485449

1108485448

OCLC:

1131893368