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...

This paper is a continuation of my previous paper in Mathematica Bohemica and solves the same problem but by means of another method. It deals with almost periodic solutions of a certain type of almost periodic systems of differential equations.

let x=(xi, • • ■ , xn) and /=(fi, • • • ,/„), and suppose that / is of class C1. A set, 12, of points x will be called unrestricted if, whenever a point x0 is in 12, the solution path x = x(t), where x0 = x(0), exists for — co </< oo and lies in 12. Two types of stability distinguished simply by "A" and "B" will be considered: (A) Let the value to be arbitrary but fixed. A solution x — x(t) of ...

In this paper, by applying Mawhin’s continuation theorem of coincidence degree theory, we study the existence of almost periodic solutions for neural multi-delay logarithmic population model and obtain one sufficient condition for the existence of positive almost periodic solution for the above equation. An example is employed to illustrate our result. Keywords—Almost periodic solution; Multi-d...