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...

Let fig be the Stone-Cech compactification of a group G, Aa the set of all almost periodic points in G, Ka c[U { supp eLIM(G)}] and Ra the set of all recurrent points in fiG. In this paper we will study the relationships between Ka and Ra, and between Aa and Ra. We will show that for any infinite elementary amenable group G, Aa Ra and RaKa =/= .

This paper concerns the square-mean almost periodic solutions to a class of nonautonomous stochastic differential equations on a separable real Hilbert space. Using the so-called ‘Acquistapace-Terreni’ conditions, we establish the existence and uniqueness of a square-mean almost periodic mild solution to those nonautonomous stochastic differential equations.

Our goal in this paper is to exhibit a connection between two seemingly disparate areas: Ramsey theory and the theory of unitary representations of a class of locally compact groups. The class of groups that we are interested in consists of the so-called ”minimally periodic groups” introduced by von Neumann in [N]; namely, groups having the property that they do not admit non-trivial almost per...

In this paper we discuss some results of the theory of holomorphic almost periodic functions on coverings of complex manifolds, recently developed by the authors. The methods of the proofs are mostly sheaf-theoretic which allows us to obtain new results even in the classical setting of H. Bohr’s holomorphic almost periodic functions on tube

Let β > 1 be a real number and M : R → GL(C) be a uniformly almost periodic matrix-valued function. We study the asymptotic behavior of the product Pn(x) = M(β x) · · ·M(βx)M(x). Under some condition we prove a theorem of Furstenberg-Kesten type for such products of non-stationary random matrices. Theorems of Kingman and Oseledec type are also proved. The obtained results are applied to multipl...