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Operator Analysis
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Operator Analysis : Hilbert Space Methods in Complex Analysis

by Jim Agler , John Edward McCarthy , Nicholas John Young

Book Details

Format Hardback or Cased Book
Book Series Cambridge Tracts in Mathematics
ISBN-10 1108485448
ISBN-13 9781108485449
Publisher Cambridge University Press
Imprint Cambridge University Press
Country of Manufacture GB
Country of Publication GB
Publication Date Mar 26th, 2020
Print length 388 Pages
Weight 728 grams
Dimensions 23.60 x 15.80 x 3.20 cms
Product Classification: Complex analysis, complex variables Functional analysis & transforms
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This monograph, aimed at graduate students and researchers, explores the use of Hilbert space methods in function theory. Explaining how operator theory interacts with function theory in one and several variables, the authors journey from an accessible explanation of the techniques to their uses in cutting edge research.
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.

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