Stability of Operators and Operator Semigroups [Hardcover]

The asymptotic behaviour, in particular stability in some sense, is studied systematically for discrete and for continuous linear dynamical systems on Banach spaces. Of particular concern is convergence to an equilibrium with respect to various topologies. Parallels and differences between the discrete and the continuous situation are emphasised.

This book systematically studies the asymptotic behavior, in particular stability in some sense, for discrete and continuous linear dynamical systems on Banach spaces. Of special concern is convergence to an equilibrium regarding various topologies.

The asymptotic behaviour, in particular stability in some sense, is studied systematically for discrete and for continuous linear dynamical systems on Banach spaces. Of particular concern is convergence to an equilibrium with respect to various topologies. Parallels and differences between the discrete and the continuous situation are emphasised.

Introduction.- Chapter I. Functional analytic tools.- 1. Structure of compact semigroups.- 2. Mean ergodicity.- 3. Tools from semigroup theory.- Chapter II. Stability of linear operators.- 1. Power boundedness.- 2. Strong stability.- 3. Weak stability.- 4. Almost weak stability.- 5. Abstract examples.- 6. Stability via Lyapunov equation.- Chapter III. Stability of C0-semigroups.- 1. Boundedness.- 2. Uniform exponential stability.- 3. Strong stability.- 4. Weak stability.- 5. Almost weak stability.- 6. Abstract examples.- 7. Stability via Lyapunov equation.- Chapter IV. Discrete vs. continuous.- 1. Embedding operators into C0-semigroups.- 2. Cogenerators.- Bibliography.

From the book reviews:

This nice volume gives a good introduction to the asymptotic behaviour of linear dynamical systems. & This volume leads to the frontiers of recent research in a rapidly developing area of mathematics. It can be warmly recommended to researchers and graduate studenl³2