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Numerical Range of Holomorphic Mappings and Applications

  • Mark Elin
  • Simeon Reich
  • David Shoikhet

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Mark Elin, Simeon Reich, David Shoikhet
    Pages 1-20
  3. Mark Elin, Simeon Reich, David Shoikhet
    Pages 21-62
  4. Mark Elin, Simeon Reich, David Shoikhet
    Pages 63-95
  5. Mark Elin, Simeon Reich, David Shoikhet
    Pages 97-128
  6. Mark Elin, Simeon Reich, David Shoikhet
    Pages 129-164
  7. Mark Elin, Simeon Reich, David Shoikhet
    Pages 165-205
  8. Back Matter
    Pages 207-229

About this book

Introduction

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.

 

Keywords

numerical range holomorphic mapping semigroup fixed point infinitesimal generator dissipative mapping Lumer-Phillips theorem

Authors and affiliations

  • Mark Elin
    • 1
  • Simeon Reich
    • 2
  • David Shoikhet
    • 3
  1. 1.Department of MathematicsORT Braude CollegeKarmielIsrael
  2. 2.Department of MathematicsThe Technion - Israel Institute of TechnologyHaifaIsrael
  3. 3.Department of Mathematics ORT Braude College Karmiel, IsraelDepartment of Mathematics, Holon Institute of TechnologyHolonIsrael

Bibliographic information