Topics in Operator Semigroups

  • Shmuel Kantorovitz

Part of the Progress in Mathematics book series (PM, volume 281)

Table of contents

  1. Front Matter
    Pages 1-11
  2. General Theory

    1. Front Matter
      Pages 1-1
    2. Shmuel Kantorovitz
      Pages 3-48
    3. Shmuel Kantorovitz
      Pages 49-61
    4. Shmuel Kantorovitz
      Pages 63-69
    5. Shmuel Kantorovitz
      Pages 71-86
    6. Shmuel Kantorovitz
      Pages 87-112
    7. Shmuel Kantorovitz
      Pages 113-130
    8. Shmuel Kantorovitz
      Pages 131-138
  3. Integral Representations

    1. Front Matter
      Pages 140-140
    2. Shmuel Kantorovitz
      Pages 141-160
    3. Shmuel Kantorovitz
      Pages 161-175
    4. Shmuel Kantorovitz
      Pages 177-190
  4. A Taste of Applications

    1. Front Matter
      Pages 194-195
    2. Shmuel Kantorovitz
      Pages 195-201
    3. Shmuel Kantorovitz
      Pages 203-218
  5. Back Matter
    Pages 1-47

About this book


The theory of operator semigroups was essentially discovered in the early 1930s.  Since then, the theory has developed into a rich and exciting area of functional analysis and has been applied to various mathematical topics such as Markov processes, the abstract Cauchy problem, evolution equations, and mathematical physics.

This self-contained monograph focuses primarily on the theoretical connection between the theory of operator semigroups and spectral theory. Divided into three parts with a total of twelve distinct chapters, this book gives an in-depth account of the subject with numerous examples, detailed proofs, and a brief look at a few applications.

Topics include:

* The Hille–Yosida and Lumer–Phillips characterizations of semigroup generators

* The Trotter–Kato approximation theorem

* Kato’s unified treatment of the exponential formula and the Trotter product formula

* The Hille–Phillips perturbation theorem, and Stone’s representation of unitary semigroups

*  Generalizations of spectral theory’s connection to operator semigroups

* A natural generalization of Stone’s spectral integral representation to a Banach space setting

With a collection of miscellaneous exercises at the end of the book and an introductory chapter examining the basic theory involved, this monograph is suitable for second-year graduate students interested in operator semigroups.


Nussbaum’s theorem Stone’s representation Trotter product formula Trotter--Kato approximation theorem functional analysis operator semigroups spectral theory unitary semigroups

Authors and affiliations

  • Shmuel Kantorovitz
    • 1
  1. 1.Dept. Mathematics & Computer ScienceBar-Ilan UniversityRamat GanIsrael

Bibliographic information

  • DOI
  • Copyright Information Birkhäuser Boston 2010
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4931-9
  • Online ISBN 978-0-8176-4932-6
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site