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  3. Operator Analysis
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    • Publisher:
      Cambridge University Press
      Publication date:
      March 2020
      March 2020
      ISBN:
      9781108751292
      9781108485449
      DOI:
      https://doi.org/10.1017/9781108751292
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.66kg, 388 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis
      Series:
      Cambridge Tracts in Mathematics (219)
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis
    Series:
    Cambridge Tracts in Mathematics (219)
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    Book description

    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.

    Reviews

    ‘This is a much awaited book, which brings together several results obtained in the last decades, pertaining to the applications of operator theory in Hilbert space to function theory … The book is extremely nicely written. It does not need many prerequisites, besides elementary facts of complex analysis and functional analysis; and it can be of much use to interested researchers as well as to graduate students.’

    Dan Timotin Source: zbMATH

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