Related papers: Universality of almost periodic orbits in certain …

In this paper a new class of radial basis functions based on hyperbolic trigonometric functions will be introduced and studied. We focus on the properties of their generalised Fourier transforms with asymptotics. Therefore we will compute…

The main theme of this paper is a relative version of the almost existence theorem for periodic orbits of autonomous Hamiltonian systems. We show that almost all low levels of a function on a geometrically bounded symplectically aspherical…

In this paper we introduce an equivalence relation on the classes of almost periodic functions of a real or complex variable which is used to refine Bochner's result that characterizes these spaces of functions. In fact, with respect to the…

In this paper, we consider composition principles for generalized almost periodic functions. We prove several new composition principles for the classes of (asymptotically) Stepanov $p$-almost periodic functions and (asymptotically,…

We introduce and study a dimensional-like characteristic of an uniformly almost periodic function, which we call the Diophantine dimension. By definition, it is the exponent in the asymptotic behavior of the inclusio length. Diophantine…

We consider non oscillatory functions and prove an everywhere Fourier Inversion Theorem for functions of very moderate decrease. The proofs rely on some ideas in nonstandard analysis.

In this paper, the notion of simultaneous universality is introduced, concerning operators having orbits that simultaneously approximate any given vector. This notion is related to the well known concepts of universality and disjoint…

Given a charge and current distribution with compact support, the associated potentials and fields are generally not integrable in the classical sense. However, it is convenient to be able to define their Fourier transform in order to…

We prove the existence of an effective universal upper bound for the order of any integral periodic orbit of any integral algebraic dynamical system in a fixed ambient space. Using this, we demonstrate the decidability of periodicity in…

We introduce the notion of "quasi-symmetric" polynomials, which is a generalization of the notion of symmetry, and is particularly suited to the setting of polynomial rings over finite fields. The properties of this new class of functions…

Unstable operations in a generalized cohomology theory E give rise to a functor from the category of algebras over E to itself which is a colimit of representable functors and a comonoid with respect to composition of such functors. In this…

The true- and eccentric-anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits by considering perturbations of the radial part of kinetic energy as a series in the negative powers of the orbital radius. A…

Indicator functions mentioned in the title are constructed on an arbitrary nondiscrete locally compact Abelian group of finite dimension. Moreover, they can be obtained by small perturbation from any indicator function fixed beforehand. In…

Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…

We present a method for constructing superoscillatory functions the superoscillatory part of which approximates a given polynomial with arbitrarily small error in a fixed interval. These functions are obtained as the product of the…

In this introductory paper we study nearly Frobenius algebras which are generalizations of the concept of a Frobenius algebra which appear naturally in topology: nearly Frobenius algebras have no traces (co-units). We survey the most basic…

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.

This paper deals with the set of the real projections of the zeros of an arbitrary almost periodic function defined in a vertical strip $U$. It provides practical results in order to determine whether a real number belongs to the closure of…

Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…

Various versions of the classical definitions of (one- and twosided) almost periodicity for functions on groups with values in a uniform space are formulated and their equivalence is shown.