Operator analysis: Hilbert space methods in complex analysis
by Agler, Jim
"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…
Read More ↓Title Statements
- Full title :Operator analysis : Hilbert space methods in complex analysis / Jim Agler, John Edward McCarthy, Nicholas Young.
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"--
Read More ↓Edition Statements
- Publication Date:2020.
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge, United Kingdom
- Language:eng
- Publication Date:2020.
The Physical Object
- Description:XV, 375 p. : : il. ; : 24 cm
Edition Identifiers
- ISBN:9781108485449, 1108485448
- oclc:on1193315870
- LC Classification:QA329
Table of 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.
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