-regularized -resolvent families: regularity and local properties.
A discrete Lyapunov theorem for the exponential stability of evolution families.
Almost periodicity of C-semigroups, integrated semigroups and C-cosine functions
We investigate the characterization of almost periodic C-semigroups, via the Hille-Yosida space Z₀, in case of R(C) being non-dense. Analogous results are obtained for C-cosine functions. We also discuss the almost periodicity of integrated semigroups.
Asymptotic almost periodicity of -semigroups.
-continuity of the Fröbenius-Perron semigroup.
C0-semigroups norm continuous at infinity.
C-Distribution semigroups
A class of C-distribution semigroups unifying the class of (quasi-) distribution semigroups of Wang and Kunstmann (when C = I) is introduced. Relations between C-distribution semigroups and integrated C-semigroups are given. Dense C-distribution semigroups as well as weak solutions of the corresponding Cauchy problems are also considered.
Composition property and automatic extension of local convoluted -cosine functions
Convoluted -groups
Convoluted C-operator families and abstract Cauchy problems
Equilibrium points for a wave equation with boundary control containing an integral term. (Points d'équilibre pour une équation des ondes avec contrôle frontière contenant un terme intégral.)
Fractional evolution equations governed by coercive differential operators.
Inverses of generators of nonanalytic semigroups
Suppose A is an injective linear operator on a Banach space that generates a uniformly bounded strongly continuous semigroup . It is shown that generates an -regularized semigroup. Several equivalences for generating a strongly continuous semigroup are given. These are used to generate sufficient conditions on the growth of , on subspaces, for generating a strongly continuous semigroup, and to show that the inverse of -d/dx on the closure of its image in L¹([0,∞)) does not generate a strongly...
Local integrated C-semigroups
We introduce the notion of a local n-times integrated C-semigroup, which unifies the classes of local C-semigroups, local integrated semigroups and local C-cosine functions. We then study its relations to the C-wellposedness of the (n + 1)-times integrated Cauchy problem and second order abstract Cauchy problem. Finally, a generation theorem for local n-times integrated C-semigroups is given.
Locally Lipschitz continuous integrated semigroups
This paper is concerned with the problem of real characterization of locally Lipschitz continuous (n + 1)-times integrated semigroups, where n is a nonnegative integer. It is shown that a linear operator is the generator of such an integrated semigroup if and only if it is closed, its resolvent set contains all sufficiently large real numbers, and a stability condition in the spirit of the finite difference approximation theory is satisfied.
Notes on Analytic Convoluted -semigroups
On a theorem of Zabczyk for semigroups of operators in locally convex spaces.
On -bounded semigroups as a generalization of -semigroups.
On local -times integrated -semigroups.
On regularized quasi-semigroups and evolution equations.