Related papers: Definitions of almost periodicity
In this paper we establish a new equivalence relation on the spaces of almost periodic functions which allows us to prove a result like Bohr's equivalence theorem extended to the case of all these functions.
We present a unified theory for the almost periodicity of functions with values in an arbitrary Banach space, measures and distributions via almost periodic elements for the action of a locally compact abelian group on a uniform topological…
Uniqueness theorems are considered for various types of almost periodic objects: functions, measures, distributions, multisets, holomorphic and meromorphic functions.
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
In this paper, we introduce several various classes of $c$-almost periodic type functions and their Stepanov generalizations, where $c\in {\mathbb C}$ and $|c|=1.$ We also consider the corresponding classes of $c$-almost periodic type…
We provide an introduction of some basic facts of uniformly almost periodic functions, such as Fourier series representations. A result is then proved about Fourier coefficients which is a generalization of the purely periodic case. We then…
We present a notion of almost periodicity wich can be applied to random dynamical systems as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations). This concept…
In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…
Whenever all differences between zeros of two holomorphic almost periodic functions in a strip form a discrete set, then both functions are infinite products of periodic functions with commensurable periods. In particular, the result is…
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 first propose two types of concepts of almost periodic functions on the quantum time scale. Secondly, we study some basic properties of almost periodic functions on the quantum time scale. Thirdly, based on these, we study…
In this paper, we first give the definition of random almost periodic solutions of random dynamical systems and give some examples. Then, we prove the existence of such random almost periodic solutions. Further, we introduce the definition…
The almost periodic functions form a natural example of a non-separable normed space. As such, it has been a challenge for constructive mathematicians to find a natural treatment of them. Here we present a simple proof of Bohr's fundamental…
In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous…
This is a brief survey of up-to-date results on holomorphic almost periodic functions and mappings in one and several complex variables, mainly due to the Kharkov mathematical school.
Almost periodicity has been considered in Formal Language Theory in connection with some topics in Symbolic Dynamics. In (P\u{a}un and Marcus, Bulletin of EATCS 53 (1994)) some problems concerning this property are raised. For instance it…
We prove that almost periodicity in the sense of distributions coincides with almost periodicity with respect to Stepanov's metric for the class of subharmonic functions in a horizontal strip. We also prove that Fourier coefficients of…
In topological dynamics, the dynamical behavior sometimes has a sharp contrast when the action is by semigroups or monoids to when the action is by groups. In this article we bring out this contrast while discussing the equivalence of…
Using a special metric in the space of sequences, we give a geometric description of almost periodic sets in the $k$-dimensional Euclidean space. We prove the completeness of the space of almost periodic sets and some analogue of the…
The notions of almost periodicity in the sense of Weyl and Besicovitch of the order p are extended to holomorphic functions on a strip. We prove that the spaces of holomorphic almost periodic functions in the sense of Weyl for various…