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The Integration of Stepanov Remotely Almost Periodic Functions

David Cheban

Abstract

The aim of this paper is to study the problem of the integration of Stepanov remotely almost periodic functions. We prove that every compact primitive of a Stepanov remotely almost periodic function with a minimal $ω$-limit set is remotely almost periodic. This fact proves the conjecture previously formulated by the author.

The Integration of Stepanov Remotely Almost Periodic Functions

Abstract

The aim of this paper is to study the problem of the integration of Stepanov remotely almost periodic functions. We prove that every compact primitive of a Stepanov remotely almost periodic function with a minimal -limit set is remotely almost periodic. This fact proves the conjecture previously formulated by the author.
Paper Structure (13 sections, 35 theorems, 69 equations)

This paper contains 13 sections, 35 theorems, 69 equations.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Remotely almost periodic motions of dynamical systems
  4. Remotely Almost Periodic Functions
  5. $S^{p}$ remotely almost periodic functions
  6. Shift dynamical systems on the space $L_{loc}^p(\mathbb{R};\mathfrak{B};\mu).$
  7. Stepanov remotely almost periodic functions
  8. Some properties of $S^{p}$ remotely almost periodic functions
  9. Integration of $S^{p}$ remotely almost periodic functions
  10. Examples
  11. Funding
  12. Data availability
  13. Conflict of Interest

Key Result

Theorem 2.2

Che_2009 A point $x\in X$ is asymptotically $\tau$-periodic if and only if the sequences $\{\pi(k\tau,x)\}_{k=0}^{\infty}$ converges.

Theorems & Definitions (81)

  • Definition 2.1
  • Theorem 2.2
  • Definition 2.3
  • Definition 2.4
  • Remark 2.5
  • Definition 2.6
  • Theorem 2.7
  • Definition 2.8
  • Corollary 2.9
  • proof
  • ...and 71 more