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On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm

Fazia Bedouhene, Mohamed Morsli, Mannal Smaali (2010)

Commentationes Mathematicae Universitatis Carolinae

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, H -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 k-convexity of the Besicovitch-Orlicz space of almost periodic functions with the Orlicz norm

Fazia Bedouhene, Mohamed Morsli (2007)

Colloquium Mathematicae

Boulahia and the present authors introduced the Orlicz norm in the class B ϕ -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 B ϕ -a.p. with respect to the Orlicz norm; we give necessary and sufficient conditions in terms of strict convexity and reflexivity.

On the uniqueness of periodic decomposition

Viktor Harangi (2011)

Fundamenta Mathematicae

Let a ₁ , . . . , a k be arbitrary nonzero real numbers. An ( a ₁ , . . . , a k ) -decomposition of a function f:ℝ → ℝ is a sum f ₁ + ⋯ + f k = f where f i : ℝ → ℝ is an a i -periodic function. Such a decomposition is not unique because there are several solutions of the equation h ₁ + ⋯ + h k = 0 with h i : ℝ → ℝ a i -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 ( a ₁ , . . . , a k ) -decomposition is essentially unique. We characterize those periods for which essential uniqueness...

Quasicrystals and almost periodic functions

Mariusz Zając (1999)

Annales Polonici Mathematici

We consider analogies between the "cut-and-project" method of constructing quasicrystals and the theory of almost periodic functions. In particular an analytic method of constructing almost periodic functions by means of convolution is presented. A geometric approach to critical points of such functions is also shown and illustrated with examples.

Remarques sur un théorème de J. Delsarte

Yves Meyer (1976)

Annales de l'institut Fourier

On donne une démonstration nouvelle (et un peu plus générale) d’un théorème de J. Delsarte sur les fonctions moyenne-périodiques de deux variables.

Remotely c -almost periodic type functions in ℝ n

Marco Kostić, Vipin Kumar (2022)

Archivum Mathematicum

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 quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely c -almost periodic functions in ℝ n , slowly oscillating functions in ℝ n , and further analyze the recently introduced class of quasi-asymptotically c -almost periodic functions...

Currently displaying 61 – 80 of 99