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Exponentially Dichotomous Operators and Applications

  • Book
  • © 2008

Overview

Authors:
  1. Cornelis Mee

    1. Dipartimento di Matematica e Informatica, Università di Cagliari, Cagliari, Italy

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  • First book at graduate level on autonomous first-order differential equations with exponential dichotomy in a Banach space
  • Includes supplementary material: sn.pub/extras

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

Part of the book sub series: Linear Operators and Linear Systems (LOLS)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xv
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  2. Exponentially Dichotomous operators and Bisemigroups

    Pages 1-25

  3. Perturbing Exponentially Dichotomous Operators

    Pages 27-46

  4. Abstract Cauchy problems

    Pages 47-59

  5. Riccati Equations and Wiener-Hopf Factorization

    Pages 61-87

  6. Transport Equations

    Pages 89-114

  7. Indefinite Sturm-Liouville Problems

    Pages 115-137

  8. Noncausal Continuous Time Systems

    Pages 139-187

  9. Mixed-type Functional Differential Equations

    Pages 189-207

  10. Back Matter

    Pages 209-224
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Keywords

About this book

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.

Authors and Affiliations

  • Dipartimento di Matematica e Informatica, Università di Cagliari, Cagliari, Italy

    Cornelis Mee

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