Operator Analysis - Jim Agler

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Résumé :
A detailed monograph exploring how operator theory interacts with function theory in one and several variables.

Biographie:
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).

Sommaire:
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. Carath?odory-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.