On omega limiting sets of infinite dimensional Volterra operators

Farrukh Mukhamedov, Otabek Khakimov, Ahmad Fadillah Embong

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In the present paper, we are aiming to study limiting behaviour of infinite dimensional Volterra operators. We introduce two classes V-+ and V-− of infinite dimensional Volterra operators. For operators taken from the introduced classes we study their omega limiting sets ωV and ωV(w) with respect to ℓ1-norm and pointwise convergence, respectively. To investigate the relations between these limiting sets, we study linear Lyapunov functions for such kind of Volterra operators. It is proven that if Volterra operator belongs to V-+, then the sets ωV (x) and ωV(w)(x) coincide for every x ∈ S, and moreover, they are non empty. If Volterra operator belongs to V-−, then ωV(x) could be empty, and it implies the non-ergodicity (w.r.t. ℓ1-norm) of V, while it is weak ergodic.

Original languageEnglish
Pages (from-to)5875-5904
Number of pages30
JournalNonlinearity
Volume33
Issue number11
DOIs
Publication statusPublished - Nov 2020

Keywords

  • Ergodic
  • Infinite dimensional
  • Omega limiting sets
  • Volterra operator

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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