This paper is concerned with the behavior of semigroups of nonlinear contractions on closed convex subsets of a Hilbert space H. Recently, many results, known for semigroups of linear operators, were extended to semigroups of nonlinear contractions. The first results in this direction by Neuberger [25] and oharu [26] dealt mainly with the representation of such semigroups by means of exponentia...

This paper is concerned with nonautonomous differential equations in Banach spaces. Using the theory of semigroups of linear and nonlinear operators one investigates the semigroups of weighted translation operators associated with the underlying equations. Necessary and sufficient conditions for different types of stability are given in terms of spectral properties of the translation operators ...

Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study a class of semigroups on such dual pairs which are an abstract version of transition semigroups. Using our results, we prove conditions ensuring that a ...

In this paper, varieties of completely regular semigroups are studied. This paper is divided into six sections. Section 1 contains an introduction to varieties of completely regular semigroups and preliminaries. Most of the notation needed in this paper is given. In Section 2, the operators ←− ( ) and −→ ( ) on the lattice of subvarieties of varieties of completely regular semigroups are invest...

This paper is concerned with characterizations of those linear, closed, but not necessarily densely defined operators A on a Banach space E with nonempty resolvent set for which the abstract Cauchy problem u'(t) = Au(t), u(0) = x has unique, exponentially bounded solutions for every initial value x e D(A). Investigating these operators we are led to the class of "integrated semigroups". Among o...

The purpose of this paper is to extend a stability theorem of Zabczyk to the case of semigroups of operators in locally convex topological vector spaces. Obtained results generalize the similar theorems proved by Datko, Pazy, Rolewicz and Littman for the case of C0-semigroups of operators in Banach spaces. AMS Mathematics Subject Classification (2000): 34D05,34D20

Our goal is to define exponentials of linear operators. We will try to construct etA as a linear operator, where A : D(A)→ X is a general linear operator, not necessarily bounded. Notationally, it seems like we are looking for a solution to μ̇(t) = Aμ(t), μ(0) = μ0, and we would like to write μ(t) = eμ0. It turns out that this will hold once we make sense of the terms. How can we construct etA w...

This is a survey on recent developments of the theory of one-parameter semigroups and evolution equations with special emphasis on functional calculus and kernel estimates. Also other topics as asymptotic behavior for large time and holomorphic semigroups are discussed. As main application we consider elliptic operators with various boundary conditions. Semigroups and evolution equations: Funct...