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On omega limiting sets of infinite dimensional Volterra operators
| Content Provider | Scilit |
|---|---|
| Author | Mukhamedov, Farrukh Khakimov, Otabek Embong, Ahmad Fadillah |
| Copyright Year | 2020 |
| Description | Journal: Nonlinearity In the present paper, we are aiming to study limiting behaviour of infinite dimensional Volterra operators. We introduce two classes and of infinite dimensional Volterra operators. For operators taken from the introduced classes we study their omega limiting sets $ω_{V }$ and with respect to $ℓ^{1}$-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 , then the sets and coincide for every x ∈ S, and moreover, they are non empty. If Volterra operator belongs to , then $ω_{V }$(x) could be empty, and it implies the non-ergodicity (w.r.t. $ℓ^{1}$-norm) of V, while it is weak ergodic. |
| Related Links | https://iopscience.iop.org/article/10.1088/1361-6544/ab9a1c/pdf |
| Ending Page | 5904 |
| Page Count | 30 |
| Starting Page | 5875 |
| ISSN | 09517715 |
| e-ISSN | 13616544 |
| DOI | 10.1088/1361-6544/ab9a1c |
| Journal | Nonlinearity |
| Issue Number | 11 |
| Volume Number | 33 |
| Language | English |
| Publisher | IOP Publishing |
| Publisher Date | 2020-10-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Nonlinearity Applied Mathematics Dimensional Volterra Operators Infinite Dimensional Volterra |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistical and Nonlinear Physics Mathematical Physics |
