Let G be a locally compact group, and consider the weakly-almost periodic functionals on M(G), the measure algebra of G, denoted by WAP(M(G)). This is a C∗-subalgebra of the commutative C∗-algebra M(G)∗, and so has character space, say K. In this paper, we investigate properties of K. We present two proofs, one using tensor product techniques, and the other using vector-valued integration, to s...

1. Several procedures have been devised to establish the existence of an invariant mean for almost periodic functions on a group (see [l; 3; 4; 5]).1 The object of the present short note is to prove this basic result concerning such functions in another way. Throughout what follows the formula (x): A—*B regarding a function (x) will be used to imply that <p(x) is defined on a set A and ha...

This work is concernedwith a class of fourth order semilinear ordinary differential equation with pseudo almost periodic environment and multiple delays. Specifically, we establish the existence and uniqueness of the pseudo almost periodic solutions. Furthermore, we discuss the global stability of the considered equation.

Recently, authors [2] have discussed some equivalent relations for ρ-uniform stabilities of a given equation and those of its limiting equations by using the skew product flow constructed by quasi-processes on a general metric space. In 1992, Murakami and Yoshizawa [6] pointed out that for functional differential equations with infinite delay on a fading memory space B = B((−∞, 0];R) ρ-stabilit...

We introduce a new invariant S (M) for type III factors M with no almost-periodic weights. We compute this invariant for certain free Araki-Woods factors. We show that Connes’ invariant τ cannot distinguish all isomorphism classes of free Araki-Woods factors. We show that there exists a continuum of mutually non-isomorphic free Araki-Woods factors, each without almostperiodic weights.

2. A topological classification of the almost periodic homeomorphisms on a closed 2-cell. A homeomorphism A of a metric space (X, p) onto itself is said to be almost periodic on X if €>0 implies that there exists a relatively dense sequence {«¿} of integers such that p(x, A"*'(x)) <e for all xGA and i= ±1, ±2, • • •. A homeomorphism A of the space X onto itself is said to be topologically equiv...

We investigate spectral properties of the translation action on the orbit closure of a Delone set. In particular, suucient conditions for pure discrete spectrum are given, based on the notion of almost periodicity. Connections with diiraction spectrum are discussed.

By means of Mawhin’s continuation theorem of coincidence degree theory, some new sufficient conditions are obtained for the existence of at least four positive almost periodic solutions for a harvesting mutualism model with time delays. To the best of the author’s knowledge, so far, the result of this paper is completely new. An example is employed to illustrate the result of this paper.

We present cut and project formalism based on measures and continuous weight functions of sufficiently fast decay. The emerging measures are strongly almost periodic. The corresponding dynamical systems are compact groups and homomorphic images of the underlying torus. In particular, they are strictly ergodic with pure point spectrum and continuous eigenfunctions. Their diffraction can be calcu...

In this article we study the existence of almost periodic solutions for distributed parameters biochemical system, with time delay when the input Sin is time dependent. This study is motivated by the input begin time dependent in many applications, and by the importance of almost periodically varying environments. Using the semigroup method, we prove that if the input is almost periodic then th...