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...

Almost periodic divisors, holomorphic functions, and holomorphic mappings * Favorov S.Ju. Abstract We prove that to each almost periodic, in the sense of distributions, divisor d in a tube T Ω ⊂ C m one can assign a cohomology class from H 2 (K, Z) (actually, the first Chern class of a special line bundle over K generated by d) such that the trivial cohomology class represents the divisors of a...

We consider Toeplitz operators with symbols that are almost periodic matrix functions of several variables. It is shown that under certain conditions on the group generated by the Fourier support of the symbol, a Toeplitz operator is Fredholm if and only if it is invertible.

Department of Mathematics University of British Columbia Vancouver, B.C., Canada V6T lZ2 (Received June 30, 1992 and in revised form November 7, 1992) ABSTRACT. A formula is set up between vector-vMued mean and scMax-valued that enbles translate many important results about scalar-valued means developed in [1] to vector-valued means. As applications of the theory of vector-vMued means, .how tha...