The notion of locally quasi-convex abelian group, introduce by Vilenkin, is extended to maximally almost-periodic non-necessarily abelian groups. For that purpose, we look at certain bornologies that can be defined on the set rep(G) of all finite dimensional continuous representations on a topological group G in order to associate well behaved group topologies (dual topologies) to them. As a co...

The problem of strict convexity of the Besicovitch-Orlicz space of almost periodic functions is considered here in connection with the Orlicz norm. We give necessary and sufficient conditions in terms of the function φ generating the space. 2000 Mathematics Subject Classification: 46B20, 42A75.

We study the planar problem of two satellites attracted by a center of force. Assuming that the center of mass of the two-satellite system is on a circular orbit around the center of force and using Levi-Civita regularization we prove the existence of an almost periodic orbit with an infinite number of collision between the satellites.

Let G be a locally compact group, and let A(G) and VN(G) be its Fourier algebra and group von Neumann algebra, respectively. In this paper we consider the similarity problem for A(G): Is every bounded representation of A(G) on a Hilbert space H similar to a ∗-representation? We show that the similarity problem for A(G) has a negative answer if and only if there is a bounded representation of A(...

It is sometimes claimed in the literature that subspace methods provide consistent estimates, also when the underlying observed signal has purely oscillatorymodes (or the generating system has uncontrollable eigenvalues on the unit circle) but a formal proof of this assertion does not seem to exist. In this paper, we prove consistency of subspacemethods with purely oscillatory modes. A well-kno...

Suppose that a sequence of numbers xn (a ‘signal’) is transmitted through a noisy channel. The receiver observes a noisy version of the signal with additive random fluctuations, xn + ξn, where ξn is a sequence of independent standard Gaussian random variables. Suppose further that the signal is known to come from some fixed space X of possible signals. Is it possible to fully recover the transm...