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Bouthat, Ludovick; Mashreghi, Javad et Morneau-Guérin, Frédéric (déc. 2020). The norm of an infinite L-matrix. Communication présentée à la Réunion d'hiver de la Société Mathématique du Canada 2020, Montréal.
Fichier(s) associé(s) à ce document :|
PDF
- The norm of an infinite L-matrix - CMS winter meeting 2020.pdf
Contenu du fichier : Diaporama Accès restreint jusqu'à fin- janvier 2026. |
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| Catégorie de document : | Communications à des congrès/colloques et conférences (non publiées) |
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| Évaluation par un comité de lecture : | Oui |
| Étape de publication : | Non publié |
| Résumé : | We know that any linear application from Cn to Cn can be described with an n times n square matrix. The space l2 of square-summable sequences indexed by the natural numbers is a generalization of Cn to infinite dimension. We find that the operators, in the case of l2, can be described by infinite matrices. However, not all infinite matrices gives us an operator on l2. It is natural to wonder which infinite matrices are a representation of an operator on l2, and what is their norm. Because of their applications in the problem of the caracterisation of the multipliers in the weighted Dirichlet spaces, we restrict ourselves to the case of infinite L-matrices. An infinite positive L-matrix is an infinite matrix which is defined by a sequence (a_n) of positive real numbers and which is of a prescribed form. We will use the Schur test to find some conditions on the sequence (a_n) for A to be an operator on l2 and to find an upper bound on the l2 norm of A. Moreover, we will use these tools to find the exact norm of a particular set of L-matrices. |
| Adresse de la version officielle : | https://www2.cms.math.ca/Events/Winter20/ |
| Déposant: | Morneau-Guérin, Frédéric |
| Responsable : | Frédéric Morneau-Guérin |
| Dépôt : | 30 janv. 2025 13:49 |
| Dernière modification : | 30 mars 2025 13:49 |
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