Almost periodic transformations

Some Remarks on Almost Periodic Transformations

1. Recurrent and almost periodic transformations. Notations. Let ƒ be a continuous mapping (not necessarily a homeomorphism) of a topological space X in itself (that is, f(X)QX). We say that ƒ is recurrent a t a point # £ X , or that x is recurrent under ƒ, if, given any neighbourhood U(x) of x, there exist infinitely many positive integers n for which f(x)ÇE.U(x). (This definition is equivalen...

Almost Periodic Schrödinger Operators along Interval Exchange Transformations

It is shown that Schrödinger operators, with potentials along the shift embedding of irreducible interval exchange transformations in a dense set, have pure singular continuous spectrum for Lebesgue almost all points of the interval. Such potentials are natural generalizations of the Sturmian case.

Characterization of almost maximally almost-periodic groups

Let G be an abelian group. We prove that a group G admits a Hausdorff group topology τ such that the von Neumann radical n(G, τ) of (G, τ) is non-trivial and finite iff G has a non-trivial finite subgroup. If G is a topological group, then n(n(G)) 6= n(G) if and only if n(G) is not dually embedded. In particular, n(n(Z, τ)) = n(Z, τ) for any Hausdorff group topology τ on Z. We shall write our a...

Almost Periodic Harmonizable Processes

The class of harmonizable processes is a natural extension of the class of stationary processes. This paper provides sufficient conditions for the sample paths of harmonizable processes to be almost periodic uniformly, Stepanov and Besicovitch.

Almost Periodic Compactifications