| dc.creator | Leclercq, Régis | |
| dc.creator | Zeggar, Abdellatif | |
| dc.date | 2022-09-13 | |
| dc.date.accessioned | 2022-11-15T12:37:03Z | |
| dc.date.available | 2022-11-15T12:37:03Z | |
| dc.identifier | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4559 | |
| dc.identifier | 10.22199/issn.0717-6279-4559 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/215670 | |
| dc.description | In this paper, we study the discrete cohomological equation of a contracting linear automorphism A of the Euclidean space Rd. More precisely, if δ is the cobord operator defined on the Fréchet space E = Cl (Rd) (0 ≤ l ≤ ∞) by: δ(h) = h − h ◦ A, we show that:
If E = C0(Rd), the range δ (E) of δ has infinite codimension and its closure is the hyperplane E0 consisting of the elements of E vanishing at 0. Consequently, H1 (A, E) is infinite dimensional non Hausdorff topological vector space and then the automorphism A is not cohomologically C0-stable.
If E = Cl (Rd), with 1 ≤ l ≤ ∞, the space δ (E) coincides with the closed hyperplane E0. Consequently, the cohomology space H1 (A, E) is of dimension 1 and the automorphism A is cohomologically Cl-stable. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad Católica del Norte. | en-US |
| dc.relation | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4559/4132 | |
| dc.rights | Copyright (c) 2022 Régis Leclercq, Abdellatif Zeggar | en-US |
| dc.rights | https://creativecommons.org/licenses/by/4.0 | en-US |
| dc.source | Proyecciones (Antofagasta, On line); Vol. 41 No. 5 (2022); 1075-1091 | en-US |
| dc.source | Proyecciones. Revista de Matemática; Vol. 41 Núm. 5 (2022); 1075-1091 | es-ES |
| dc.source | 0717-6279 | |
| dc.source | 10.22199/issn.0717-6279-2022-05 | |
| dc.subject | fréchet space | en-US |
| dc.subject | cohomological equation | en-US |
| dc.subject | 34C40 | en-US |
| dc.subject | 46E10 | en-US |
| dc.subject | 37C05 | en-US |
| dc.title | On the cohomological equation of a linear contraction | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
| dc.type | Peer-reviewed Article | en-US |
| dc.type | text | en-US |
