Exponentially Dichotomous Operators and Applications

  • Cornelis van der Mee

Part of the Operator Theory: Advances and Applications book series (OT, volume 182)

About this book

Introduction

In this monograph the natural evolution operators of autonomous first-order differential equations with exponential dichotomy on an arbitrary Banach space are studied in detail. Characterizations of these so-called exponentially dichotomous operators in terms of their resolvents and additive and multiplicative perturbation results are given. The general theory of the first three chapters is then followed by applications to Wiener-Hopf factorization and Riccati equations, transport equations, diffusion equations of indefinite Sturm-Liouville type, noncausal infinite-dimensional linear continuous-time systems, and functional differential equations of mixed type.

Keywords

Banach space Cauchy problem Riccati equation Sturm-Liouville operator dichotomous operator operator theory transport equations

Authors and affiliations

  • Cornelis van der Mee
    • 1
  1. 1.Dipartimento di Matematica e InformaticaUniversità di CagliariCagliariItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-7643-8732-7
  • Copyright Information Birkhäuser Verlag AG 2008
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-8731-0
  • Online ISBN 978-3-7643-8732-7
  • About this book