Wolfgang Arendt

One-parameter semigroups of positive operators

Basic results on semigroups on banach spaces.- Characterization of semigroups on banach spaces.- Spectral theory.- Asymptotics of semigroups on banach spaces.- Basic results on spaces Co(X).- Characterization of positive semigroups on Co(X).- Spectral theory of positive semigroups on Co(X).- Asymptotics of positive semigroups on Co(X).- Basic results on banach lattices and positive operators.- Characterization of positive semigroups on banach lattices.- Spectral theory of positive semigroups on banach lattices.- Asymptotics of positive semigroups on banach lattices.- Basic results on semigroups and operator algebras.- Characterization of positive semigroups on w*-algebras.- Spectral theory of positive semigroups on w*-algebras and their preduals.- Asymptotics of positive semigroups on c*-and w*-algebras.

Tauberian theorems and stability of one-parameter semigroups

The main result is the following stability theorem: Let T = (T(t))tzo be a bounded Co-semigroup on a reflexive space X. Denote by A the generator of T and by a(A) the spectrum of A. If a(A) n iR is countable and no eigenvalue of A lies on the imaginary axis, then limt BOO T(t)x = O for all x E X.

OPERATOR-VALUED FOURIER MULTIPLIERS ON PERIODIC BESOV SPACES AND APPLICATIONS

Let 1 p, q ∞, s ∈ R and let X be a Banach space. We show that the analogue of Marcinkiewicz’s Fourier multiplier theorem on Lp(T) holds for the Besov space Bs p,q(T;X) if and only if 1 < p < ∞ and X is a UMD-space. Introducing stronger conditions we obtain a periodic Fourier multiplier theorem which is valid without restriction on the indices or the space (which is analogous to Amann’s result (Math. Nachr. 186 (1997), 5–56) on the real line). It is used to characterize maximal regularity of periodic Cauchy problems.

Vector-valued holomorphic functions revisited

Abstract. Let

ASYMPTOTICALLY ALMOST PERIODIC SOLUTIONS OF INHOMOGENEOUS CAUCHY PROBLEMS ON THE HALF-LINE

\Omega \subset \C

On the o-spektrum of regular operators and the spectrum of measures

be open,X a Banach space and

Dirichlet and Neumann boundary conditions: What is in between?

W\subset X^\prime

Integral representations of resolvents and semigroups

. We show that every

Tools for maximal regularity

\sigma (X,W)\mbox{-holomorphic function } f: \Omega \to X

On lattice isomorphisms with positive real spectrum and groups of positive operators

is holomorphic if and only if every