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Operator Analysis: Hilbert Space Methods in Complex Analysis 1st Edition Jim Agler

Name: Operator Analysis: Hilbert Space Methods in Complex Analysis 1st Edition Jim Agler
SKU: EB-11043594
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Operator Analysis: Hilbert Space Methods in Complex Analysis Jim Agler Digital Instant Download

Author(s): Jim Agler, John Edward McCarthy, Nicholas John Young

ISBN(s): 9781108485449, 1108485448

File Details: PDF, 2.61 MB

Year: 2020

Language: English

SKU: EB-11043594 Category: Mathematics Tags: Hilbert Space Methods, Jim Agler, John Edward McCarthy, Nicholas John Young, Operator Analysis

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Operator Analysis: Hilbert Space Methods in Complex Analysis 1st Edition Jim Agler- Ebook Instant Download/Delivery ISBN(s): 9781108485449,1108485448

Product details:

ISBN 10:1108485448
ISBN 13: 9781108485449
Author: Jim Agler, John Edward McCarthy, Nicholas John Young

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-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.

Table contents:

Part I. Commutative Theory: 1. The origins of operator-theoretic approaches to function theory

2. Operator analysis on D: model formulas, lurking Isometries, and positivity arguments

3. Further development of models on the disc

4. Operator analysis on D2

5. Carathéodory-Julia theory on the disc and the bidisc

6. Herglotz and Nevanlinna representations in several variable

7. Model theory on the symmetrized bidisc

8. Spectral sets: three case studies

9. Calcular norms; 10. Operator monotone functions

Part II. Non-Commutative Theory: 11. Motivation for non-commutative functions

12. Basic properties of non-commutative functions