On omega limiting sets of infinite dimensional Volterra operators
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...
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my.utm.906402021-04-30T14:48:23Z http://eprints.utm.my/id/eprint/90640/ On omega limiting sets of infinite dimensional Volterra operators Mukhamedov, Farrukh Khakimov, Otabek Embong, Ahmad Fadillah QA Mathematics 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. IOP Publishing Ltd 2020-11 Article PeerReviewed Mukhamedov, Farrukh and Khakimov, Otabek and Embong, Ahmad Fadillah (2020) On omega limiting sets of infinite dimensional Volterra operators. Nonlinearity, 33 (11). pp. 5875-5904. ISSN 0951-7715 http://dx.doi.org/10.1088/1361-6544/ab9a1c |
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QA Mathematics Mukhamedov, Farrukh Khakimov, Otabek Embong, Ahmad Fadillah On omega limiting sets of infinite dimensional Volterra operators |
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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. |
format |
Article |
author |
Mukhamedov, Farrukh Khakimov, Otabek Embong, Ahmad Fadillah |
author_facet |
Mukhamedov, Farrukh Khakimov, Otabek Embong, Ahmad Fadillah |
author_sort |
Mukhamedov, Farrukh |
title |
On omega limiting sets of infinite dimensional Volterra operators |
title_short |
On omega limiting sets of infinite dimensional Volterra operators |
title_full |
On omega limiting sets of infinite dimensional Volterra operators |
title_fullStr |
On omega limiting sets of infinite dimensional Volterra operators |
title_full_unstemmed |
On omega limiting sets of infinite dimensional Volterra operators |
title_sort |
on omega limiting sets of infinite dimensional volterra operators |
publisher |
IOP Publishing Ltd |
publishDate |
2020 |
url |
http://eprints.utm.my/id/eprint/90640/ http://dx.doi.org/10.1088/1361-6544/ab9a1c |
_version_ |
1698696964682547200 |
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13.154949 |