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Operator analysis : hilbert space methods in complex analysis

By: Agler, JimContributor(s): McCarthy, John E. (John Edward) | Young, NicholasMaterial type: TextTextLanguage: English Series: Cambridge tracts in mathematics ; 219Publication details: Cambridge : Cambridge University Press, 2020. Description: xv, 375p. : illustrations ; 24 cmISBN: 9781108485449Subject(s): Operator theory | Holomorphic functions | Geometric function theory | Hilbert spaceDDC classification: 517.98 Online resources: Table of Contents | Excerpt | Reviews Summary: 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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Item type Current library Call number Status Date due Barcode
Book Book SMS Library
517.98 AGL-O (Browse shelf(Opens below)) Available 25192
Book Book SMS Library
517.98 AGL-O (Browse shelf(Opens below)) Available 25145

Includes bibliographical references and index.

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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