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

"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...

Full description

Bibliographic Details
Main Authors: Agler, Jim (Author)
McCarthy, John E. (John Edward), 1964- (Author)
Young, Nicholas (Author)
Language:English
Published: Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2020.
Series:Cambridge tracts in mathematics ; 219.
Subjects:
Operator theory.
Holomorphic functions.
Geometric function theory.
Hilbert space.
Physical Description:xv, 375 pages : illustrations ; 24 cm.
Format: Book
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.