相关论文: A generalization of Bohr's Equivalence Theorem
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.
Based on Bohr's equivalence relation which was established for general Dirichlet series, in this paper we introduce a new equivalence relation on the space of almost periodic functions in the sense of Besicovitch,…
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 note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.
Given two arbitrary almost periodic functions with associated Fourier exponents which are linearly independent over the rational numbers, we prove that the existence of a common open vertical strip $V$, where both functions assume the same…
The aim of this paper is to introduce and to study an algebra of almost periodic generalized functions containing the classical Bohr almost periodic functions as well as almost periodic Schwartz distributions
Let $ \mathcal{B}:=\{f(z)=\sum_{n=0}^{\infty}a_nz^n\; \mbox{with}\; |f(z)|<1\;\mbox{for all}\; z\in\mathbb{D}\} $. The improved version of the classical Bohr's inequality \cite{Bohr-1914} states that if $ f\in\mathcal{B} $, then the…
Recently the present authors established refined versions of Bohr's inequality in the case of bounded analytic functions. In this article, we state and prove a generalization of these results in a reformulated "distance form" version and…
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, first we give a new generalization of the Bohr's inequality for the class of bounded analytic functions $\mathcal{B'}$ and for the class of sense-preserving $K$-quasiconformal harmonic mappings of the form $f=h+\overline{g},$…
Bohr's classical theorem and its generalizations are now active areas of research and have been the source of investigations in numerous function spaces. In this article, we study a generalized Bohr's inequality for the class of bounded…
The main aim of this paper is to prove a generalization of the classical Bohr theorem and as an application, we obtain a counterpart of Bohr theorem for the generalized Ces\'aro operator.
We give an extension of Bochner's criterion for the almost periodic functions. By using our main result, we extend two results of A. Haraux. The first is a generalization of Bochner's criterion which is useful for periodic dynamical…
In this paper, we introduce the study of the Bohr phenomenon for a quasi-subordination family of functions, and establish the classical Bohr's inequality for the class of quasisubordinate functions. As a consequence, we improve and obtain…
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…
In this article we establish Bohr inequalities for operator valued functions, which can be viewed as the analogues of a couple of interesting results from scalar valued settings. Some results of this paper are motivated by the classical…
We consider certain finite sets of circle-valued functions defined on intervals of real numbers and estimate how large the intervals must be for the values of these functions to be uniformly distributed in an approximate way. This is used…
The following extension of Bohr's theorem is established: If a somewhere convergent Dirichlet series $f$ has an analytic continuation to the half-plane $\mathbb{C}_\theta = \{s = \sigma+it\,:\, \sigma>\theta\}$ that maps $\mathbb{C}_\theta$…
Inspired by results of Bayart on ordinary Dirichlet series $\sum a_n n^{-s}$, the main purpose of this article is to start an $\mathcal{H}_p$-theory of general Dirichlet series $\sum a_n e^{-\lambda_{n}s}$. Whereas the…
In this paper, we analyze various classes of multi-dimensional almost periodic type functions in general metric. The main classes of functions under our consideration are $({\mathrm R}, {\mathcal B},{\mathcal P},L)$-multi-almost periodic…