Od funkcí periodických ke skoroperiodickým
On a Formula for Haar Measure in Compact Groups.
On a Problem of Best Uniform Approximation and a Polynomial Inequality of Visser
In this paper, a generalization of a result on the uniform best approximation of α cos nx + β sin nx by trigonometric polynomials of degree less than n is considered and its relationship with a well-known polynomial inequality of C. Visser is indicated.
On a Theorem of Ingham.
On Hartman almost periodic functions
We consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in or . We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally compact, abelian groups are considered. We define generalized Marcinkiewicz spaces based upon arbitrary measure spaces...
On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions
We investigate some convergence questions in the class of Besicovitch-Orlicz spaces of vector valued functions. Next, the existence problem of the projection operator on closed convex subsets is considered in the class of almost periodic functions. This problem was considered in [5], in the case of an Orlicz space. The approximation property obtained in both cases are of the same kind. However, the arguments which are used in the proofs are different.
On some classes of almost periodic functions in abstract spaces.
On some convexity properties in the Besicovitch-Musielak-Orlicz space of almost periodic functions with Luxemburg norm
In this article, it is shown that geometrical properties such as local uniform convexity, mid point local uniform convexity, H-property and uniform convexity in every direction are equivalent in the Besicovitch-Musielak-Orlicz space of almost periodic functions endowed with the Luxemburg norm.
On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm
The paper is concerned with the characterization and comparison of some local geometric properties of the Besicovitch-Orlicz space of almost periodic functions. Namely, it is shown that local uniform convexity, -property and strict convexity are all equivalent. In our approach, we first prove some metric type properties for the modular function associated to our space. These are then used to prove our main equivalence result.
On the almost periodic behaviour of certain arithmetical convolutions
On the degree of strong approximation of integrable functions in Stepanov sense
Considering the class of almost periodic functions integrable in the Stepanov sense we extend and generalize certain results of the first author, as well as of L. Leindler and P. Chandra.
On the k-convexity of the Besicovitch-Orlicz space of almost periodic functions with the Orlicz norm
Boulahia and the present authors introduced the Orlicz norm in the class -a.p. of Besicovitch-Orlicz almost periodic functions and gave several formulas for it; they also characterized the reflexivity of this space [Comment. Math. Univ. Carolin. 43 (2002)]. In the present paper, we consider the problem of k-convexity of -a.p. with respect to the Orlicz norm; we give necessary and sufficient conditions in terms of strict convexity and reflexivity.
On the properties of oscillation and almost periodicity of certain convolutions
On the strict convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz norm.
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 f generating the space.
On the uniform convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz norm
In [5], we characterized the uniform convexity with respect to the Luxemburg norm of the Besicovitch-Orlicz space of almost periodic functions. Here we give an analogous result when this space is endowed with the Orlicz norm.
On the uniqueness of periodic decomposition
Let be arbitrary nonzero real numbers. An -decomposition of a function f:ℝ → ℝ is a sum where is an -periodic function. Such a decomposition is not unique because there are several solutions of the equation with -periodic. We will give solutions of this equation with a certain simple structure (trivial solutions) and study whether there exist other solutions or not. If not, we say that the -decomposition is essentially unique. We characterize those periods for which essential uniqueness...
Oscillations presque-périodiques forcées d'équations d'Euler-Lagrange