Special classes of semigroups
About: Special classes of semigroups is a research topic. Over the lifetime, 3481 publications have been published within this topic receiving 61438 citations.
Papers published on a yearly basis
29 Oct 1999
TL;DR: In this paper, Spectral Theory for Semigroups and Generators is used to describe the exponential function of a semigroup and its relation to generators and resolvents.
Abstract: Linear Dynamical Systems.- Semigroups, Generators, and Resolvents.- Perturbation and Approximation of Semigroups.- Spectral Theory for Semigroups and Generators.- Asymptotics of Semigroups.- Semigroups Everywhere.- A Brief History of the Exponential Function.
01 Jan 1995
TL;DR: Inverse semigroups as discussed by the authors are a subclass of regular semigroup classes and can be seen as semigroup amalgamations of semigroup groups, which is a special case of regular semiigroups.
Abstract: 1. Introductory ideas 2. Green's equivalences regular semigroups 3. 0-simple semigroups 4. Completely regular semigroups 5. Inverse semigroups 6. Other classes of regular semigroups 7. Free semigroups 8. Semigroup amalgams References List of symbols
01 Apr 1992
TL;DR: In this article, the authors present an overview of Semigroups of linear operators and their relation to a parameter of Attractors of Differentiable Semigroup and Uniform Asymptotics of Trajectories.
Abstract: Quasilinear Evolutionary Equations and Semigroups Generated by Them. Maximal Attractors of Semigroups. Attractors and Unstable Sets. Some Information on Semigroups of Linear Operators. Invariant Manifolds of Semigroups and Mapping at Equilibrium Points. Steady-state Solutions. Differentiability of Operators of Semigroups Generated by Partial Differential Equations. Semigroups Depending on a Parameter. Dependence on a Parameter of Attractors of Differentiable Semigroups and Uniform Asymptotics of Trajectories. Hausdorff Dimension of Attractors. Bibliography. Index.
14 Jul 2009
TL;DR: The main topics of interest about observation and control operators are admissibility, observability, controllability, stabilizability and detectability as discussed by the authors, which is a mature area of functional analysis, which is still very active.
Abstract: The evolution of the state of many systems modeled by linear partial diﬁerentialequations (PDEs) or linear delay-diﬁerential equations can be described by operatorsemigroups. The state of such a system is an element in an inﬂnite-dimensionalnormed space, whence the name \inﬂnite-dimensional linear system".The study of operator semigroups is a mature area of functional analysis, which isstill very active. The study of observation and control operators for such semigroupsis relatively more recent. These operators are needed to model the interactionof a system with the surrounding world via outputs or inputs. The main topicsof interest about observation and control operators are admissibility, observability,controllability, stabilizability and detectability. Observation and control operatorsare an essential ingredient of well-posed linear systems (or more generally systemnodes). Inthisbookwedealonlywithadmissibility, observabilityandcontrollability.We deal only with operator semigroups acting on Hilbert spaces.This book is meant to be an elementary introduction into the topics mentionedabove. By \elementary" we mean that we assume no prior knowledge of ﬂnite-dimensional control theory, and no prior knowledge of operator semigroups or ofunbounded operators. We introduce everything needed from these areas. We doassume that the reader has a basic understanding of bounded operators on Hilbertspaces, diﬁerential equations, Fourier and Laplace transforms, distributions andSobolev spaces on