The eigenvalue distribution of products of Toeplitz matrices - clustering and attraction
| hal.structure.identifier | Department of Physics and Mathematics | |
| dc.contributor.author | SERRA-CAPIZZANO, Stefano | |
| hal.structure.identifier | Department of Physics and Mathematics | |
| dc.contributor.author | SESANA, Debora | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | STROUSE, Elizabeth | |
| dc.date.accessioned | 2024-04-04T02:44:46Z | |
| dc.date.available | 2024-04-04T02:44:46Z | |
| dc.date.created | 2010-05-01 | |
| dc.date.issued | 2010-05 | |
| dc.identifier.issn | 0024-3795 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191429 | |
| dc.description.abstractEn | We use a recent result concerning the eigenvalues of a generic (non Hermitian) complex perturbation of a bounded Hermitian sequence of matrices to prove that the asymptotic spectrum of the product of Toeplitz sequences, whose symbols have a real-valued essen- tially bounded product h, is described by the function h in the "Szeg ̈ way". Then, using Mergelyan's theorem, we extend the result to the more general case where h belongs to the Tilli class. The same technique gives us the analogous result for sequences belonging to the algebra generated by Toeplitz sequences, if the symbols associated with the sequences are bounded and the global symbol h belongs to the Tilli class. A generalization to the case of multilevel matrix-valued symbols and a study of the case of Laurent polynomials not necessarily belonging to the Tilli class are also given. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject | matrix sequence | |
| dc.subject | joint eigenvalue distribution | |
| dc.subject | Toeplitz matrix | |
| dc.title.en | The eigenvalue distribution of products of Toeplitz matrices - clustering and attraction | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.laa.2009.12.005 | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| bordeaux.journal | Linear Algebra and its Applications | |
| bordeaux.page | 2658-2678 | |
| bordeaux.volume | 432 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 10 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00338883 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00338883v1 | |
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