Jim Agler

Operator Analysis (eBook, ePUB)

Hilbert Space Methods in Complex Analysis

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 26. März 2020
• Englisch
• ISBN-13: 9781108618588
• Artikelnr.: 60863131

Autorenporträt

Jim Agler is Distinguished Professor Emeritus at the University of California, San Diego. He received the G. de B. Robinson award from the Canadian Mathematical Society in 2016 and delivered the 2017 London Mathematical Society Invited Lectures. He is the co-author of Pick Interpolation and Hilbert Function Spaces (2002).

Inhaltsangabe

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 variables
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
13. Montel theorems
14. Free holomorphic functions
15. The implicit function theorem
16. Noncommutative functional calculus
Notation.