Year: 2025
Type: article
Abstract: The purpose of this work is to study remotely almost periodic functions defined on the semi-axis ℝ + := [ 0 , + ∞ ) {\mathbb{R}_{+}:=[0,+\infty)} (respectively, on the real axis ℝ := ( - ∞ , + ∞ ) {\mathbb{R}:=(-\infty,+\infty)} ) with values in the Banach space 𝔅 {\mathfrak{B}} . We establish a relation between remotely almost periodic movements in the shift dynamical system ( C ( 𝕋 , 𝔅 ) , 𝕋 {(C(\mathbb{T},\mathfrak{B}),\mathbb{T}} , σ ) {\sigma)} ( 𝕋 = ℝ + {\mathbb{T}=\mathbb{R}_{+}} or ℝ {\mathbb{R}} ) in the space of continuous functions C ( 𝕋 , 𝔅 ) C(\mathbb{T},\mathfrak{B}) and remotely almost periodic functions. Using this connection, we prove some important analytical and topological properties of remotely almost periodic functions.
Source: Journal of Applied Analysis
Author: David Cheban
Institution: Moldova State University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403444583