Exponentially Dichotomous Operators and Applications
Mee, Cornelis
Exponentially Dichotomous Operators and Applications [electronic resource]/ by Cornelis Mee. - Basel: Birkhäuser Basel, 2008. - digital. - Operator Theory: Advances and Applications, Linear Operators and Linear Systems; 182 . - Operator Theory: Advances and Applications, Linear Operators and Linear Systems; 182 .
Preface -- 1. Exponentially Dichotomous Operators and Bisemigroups -- 2 -- Perturbing Exponentially Dichotomous Operators -- 3. Abstract Cauchy Problems -- 4. Riccati Equations and Wiener-Hopf Factorization -- 5. Transport Equations -- 6. Indefinite Sturm-Liouville Problems -- 7. Noncausal Continuous Time Systems -- 8. Mixed-type Functional Differential Equations -- Bibliography -- Index .
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 .
9783764387327
10.1007/978-3-7643-8732-7 doi
Mathematics
Operator theory.
Differential equations.
515.724
Exponentially Dichotomous Operators and Applications [electronic resource]/ by Cornelis Mee. - Basel: Birkhäuser Basel, 2008. - digital. - Operator Theory: Advances and Applications, Linear Operators and Linear Systems; 182 . - Operator Theory: Advances and Applications, Linear Operators and Linear Systems; 182 .
Preface -- 1. Exponentially Dichotomous Operators and Bisemigroups -- 2 -- Perturbing Exponentially Dichotomous Operators -- 3. Abstract Cauchy Problems -- 4. Riccati Equations and Wiener-Hopf Factorization -- 5. Transport Equations -- 6. Indefinite Sturm-Liouville Problems -- 7. Noncausal Continuous Time Systems -- 8. Mixed-type Functional Differential Equations -- Bibliography -- Index .
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 .
9783764387327
10.1007/978-3-7643-8732-7 doi
Mathematics
Operator theory.
Differential equations.
515.724