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Positive Operator Semigroups

From Finite to Infinite Dimensions

  • András Bátkai
  • Marjeta Kramar Fijavž
  • Abdelaziz Rhandi

Part of the Operator Theory: Advances and Applications book series (OT, volume 257)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Finite Dimensions

    1. Front Matter
      Pages 1-1
    2. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 3-13
    3. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 15-30
    4. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 31-42
    5. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 43-53
    6. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 55-68
    7. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 69-80
    8. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 81-91
    9. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 93-105
  3. Infinite Dimensions

    1. Front Matter
      Pages 107-107
    2. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 109-139
    3. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 141-163
    4. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 165-180
    5. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 181-195
    6. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 197-210
  4. Advanced Topics and Applications

    1. Front Matter
      Pages 211-211
    2. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 213-234
    3. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 235-252
    4. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 253-267
    5. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 269-277
    6. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 279-301
    7. András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi
      Pages 303-324
  5. Back Matter
    Pages 325-364

About this book

Introduction

This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes. 

In the first part, the finite dimensional theory in a coordinate-free way is developed, which is difficult to find in literature. This is a good opportunity to present the main ideas of the Perron-Frobenius theory in a way which can be used in the infinite dimensional situation. Applications to graph matrices, age structured population models and economic models are discussed. 

The infinite dimensional theory of positive operator semigroups with their spectral and asymptotic theory is developed in the second part. Recent applications illustrate the theory, like population equations, neutron transport theory, delay equations or flows in networks. Each chapter is accompanied by a large set of exercises. An up-to-date bibliography and a detailed subject index help the interested reader. 

The book is intended primarily for graduate and master students. The finite dimensional part, however, can be followed by an advanced bachelor with a solid knowledge of linear algebra and calculus.

Keywords

Perron-Frobenius theory asymptotic behaviour evolution equations operator semigroups positivity

Authors and affiliations

  • András Bátkai
    • 1
  • Marjeta Kramar Fijavž
    • 2
  • Abdelaziz Rhandi
    • 3
  1. 1.Pädagogische Hochschule VorarlbergFeldkirchAustria
  2. 2.Faculty of Civil and Geodetic EngineeringUniversity of LjubljanaLjubljanaSlovenia
  3. 3.Università di SalernoFiscianoItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-42813-0
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-42811-6
  • Online ISBN 978-3-319-42813-0
  • Series Print ISSN 0255-0156
  • Series Online ISSN 2296-4878
  • Buy this book on publisher's site