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Numerical Range of Holomorphic Mappings and Applications

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  • © 2019

Overview

Authors:
  1. Mark Elin

    1. Department of Mathematics, ORT Braude College, Karmiel, Israel

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  2. Simeon Reich

    1. Department of Mathematics, The Technion - Israel Institute of Technology, Haifa, Israel

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  3. David Shoikhet

    1. Department of Mathematics ORT Braude College Karmiel, Israel, Department of Mathematics, Holon Institute of Technology, Holon, Israel

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  • Explores, as a first book, the numerical range of holomorphic mappings

  • Presents in detail applications of the numerical range to solutions of diverse geometrical and analytic problems

  • Includes a survey of the theory of semigroups of linear operators including the Hille-Yosida and the Lumer-Phillips theorems

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Semigroups of Linear Operators

    • Mark Elin, Simeon Reich, David Shoikhet
    Pages 1-20

  3. Numerical Range

    • Mark Elin, Simeon Reich, David Shoikhet
    Pages 21-62

  4. Fixed Points of Holomorphic Mappings

    • Mark Elin, Simeon Reich, David Shoikhet
    Pages 63-95

  5. Semigroups of Holomorphic Mappings

    • Mark Elin, Simeon Reich, David Shoikhet
    Pages 97-128

  6. Ergodic Theory of Holomorphic Mappings

    • Mark Elin, Simeon Reich, David Shoikhet
    Pages 129-164

  7. Some Applications

    • Mark Elin, Simeon Reich, David Shoikhet
    Pages 165-205

  8. Back Matter

    Pages 207-229
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Keywords

About this book

This book describes recent developments as well as some classical results regarding holomorphic mappings. The book starts with a brief survey of the theory of semigroups of linear operators including the Hille-Yosida and the Lumer-Phillips theorems. The numerical range and the spectrum of closed densely defined linear operators are then discussed in more detail and an overview of ergodic theory is presented. The analytic extension of semigroups of linear operators is also discussed. The recent study of the numerical range of composition operators on the unit disk is mentioned. Then, the basic notions and facts in infinite dimensional holomorphy and hyperbolic geometry in Banach and Hilbert spaces are presented, L. A. Harris' theory of the numerical range of holomorphic mappings is generalized, and the main properties of the so-called quasi-dissipative mappings and their growth estimates are studied. In addition, geometric and quantitative analytic aspects of fixed point theory are discussed. A special chapter is devoted to applications of the numerical range to diverse geometric and analytic problems.

 


Reviews

“The book will serve as an excellent resource for mathematicians and applied scientists working at the frontier of the field and/or in the range of its applications. The book can also serve as an excellent graduate text for young and aspiring researchers in the field of infinite-dimensional holomorphy.” (Abebaw Tadesse, Mathematical Reviews, December, 2019)

Authors and Affiliations

  • Department of Mathematics, ORT Braude College, Karmiel, Israel

    Mark Elin

  • Department of Mathematics, The Technion - Israel Institute of Technology, Haifa, Israel

    Simeon Reich

  • Department of Mathematics ORT Braude College Karmiel, Israel, Department of Mathematics, Holon Institute of Technology, Holon, Israel

    David Shoikhet

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