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Birkhäuser - Birkhäuser Mathematics | Exponentially Dichotomous Operators and Applications

Exponentially Dichotomous Operators and Applications

van der Mee, Cornelis V. M.

2008, XV, 224 p.

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  • First book at graduate level on autonomous first-order differential equations with exponential dichotomy in a Banach space

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.

Content Level » Research

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

Related subjects » Birkhäuser Mathematics

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