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.

We study conformally invariant nonlinear wave equations in four dimensions corresponding to multicomponent massless scalar elds with a quartic interaction. We prove that the scattering operator S on the space H of nite-Einstein-energy Cauchy data has innnitely many xed points, as well as periodic points of all orders. There are also 2 H such that S n is almost periodic but not periodic, and 2 H...

We exhibit examples of almost periodic Verblunsky coefficients for which Herman’s subharmonicity argument applies and yields that the associated Lyapunov exponents are uniformly bounded away from zero. As an immediate consequence of this result, we obtain examples of almost periodic Verblunsky coefficients for which the associated probability measure on the unit circle is pure point.

We prove that the topology of the additive group of the Banach space c0 is not induced by weakly almost periodic functions or, which is the same, that this group cannot be represented as a group of isometries of a reflexive Banach space. This answers, on the negative, questions of Megrelishvili [14] and Glasner and Megrelishvili [7]. We show, in contrast, that additive groups of Schwartz locall...

We investigate second order half-linear Euler type difference equations whose coefficients have mean values. We show that these equations are conditionally oscillatory and we explicitly identify the corresponding oscillation constants given by the coefficients. Our results generalize the known ones concerning equations with positive constant, periodic, or (asymptotically) almost periodic coeffi...

We develop a quantitative version of Aubry duality and use it to obtain several sharp estimates for the dynamics of Schrödinger cocycles associated to a non-perturbatively small analytic potential and Diophantine frequency. In particular, we establish the full version of Eliasson’s reducibility theory in this regime (our approach actually leads to improvements even in the perturbative regime: w...

For the higher-order abstract differential equation u(n)(t) = Au(t) + f (t), t ∈ R, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace of BUC(R,E) with respect to the above-mentioned equation in terms of solvability of the operator equation AX −X n = C. As applications, periodicity and almost periodicity of mild solutio...

In this paper a course concept based on collaborative construction of hypervideos is presented. The course concept integrates a) hypervideo technology development, b) research on learning with hypervideo systems, and c) the application of research on knowledge acquisition by writing texts or hypertexts to hypervideos. We demonstrate how collaborative construction of hypervideo can support knowl...