Exponentially Dichotomous Operators and Applications

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.

List of contents

Exponentially Dichotomous operators and Bisemigroups.- Perturbing Exponentially Dichotomous Operators.- Abstract Cauchy problems.- Riccati Equations and Wiener-Hopf Factorization.- Transport Equations.- Indefinite Sturm-Liouville Problems.- Noncausal Continuous Time Systems.- Mixed-type Functional Differential Equations.

Summary

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.

Product details

• Authors: Cornelis V. M. van der Mee, Cornelis van der Mee, Cornelis V M van der Mee, Cornelis V. M. van der Mee
• Publisher: Springer, Basel
• Languages: English
• Product format: Hardback
• Released: 07.03.2012
• EAN: 9783764387310
• ISBN: 978-3-7643-8731-0
• No. of pages: 224
• Dimensions: 169 mm x 235 mm x 240 mm
• Weight: 544 g
• Illustrations: XV, 224 p.
• Series: Operator Theory: Advances and Applications; Linear Operators and Linear Systems; Operator Theory: Advances and Applications / Linear Operators and Linear Systems; Operator Theory: Advances and Applications; Linear Operators and Linear Systems; Operator Theory: Advances and Applications / Linear Operators and Linear Systems
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis