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Dostęp zamkniętyUni-asymptotic Linear systems and Jacobi Operators
| cris.lastimport.scopus | 2024-02-12T19:49:38Z |
| dc.abstract.en | A family {Us}s∈S of bounded linear operators in a normed space X is uni-asymptotic, when all its trajectories {Usx}s∈S with x≠0 have the same norm-asymptotic behavior (see 1.5); {Us}s∈S is tight, when the operator norm and the minimal modulus of Us have the same asymptotic behavior (see 1.6). We prove that uni-asymptoticity is equivalent to tightness if dimX<+∞, and that the finite dimension is essential. Some other conditions equivalent to uni-asymptoticity are provided, including asymptotic formulae for the operator norm and for the trajectories, expressed in terms of determinants detUs (see Theorem 1.7). We find a connection of these abstract results with some results and notions from spectral theory of Jacobi operators, e.g., with the H-class property for transfer matrix sequence. |
| dc.affiliation | Uniwersytet Warszawski |
| dc.contributor.author | Moszyński, Marcin |
| dc.date.accessioned | 2024-01-26T11:19:20Z |
| dc.date.available | 2024-01-26T11:19:20Z |
| dc.date.issued | 2019 |
| dc.description.finance | Nie dotyczy |
| dc.description.number | 3 |
| dc.description.volume | 91 |
| dc.identifier.doi | 10.1007/S00020-019-2522-6 |
| dc.identifier.issn | 0378-620X |
| dc.identifier.uri | https://repozytorium.uw.edu.pl//handle/item/124187 |
| dc.identifier.weblink | http://link.springer.com/content/pdf/10.1007/s00020-019-2522-6.pdf |
| dc.language | eng |
| dc.pbn.affiliation | mathemathics |
| dc.relation.ispartof | Integral Equations and Operator Theory |
| dc.relation.pages | 23:1-23:15 |
| dc.rights | ClosedAccess |
| dc.sciencecloud | nosend |
| dc.subject.en | Linear dynamical systems |
| dc.subject.en | Families of operators |
| dc.subject.en | Trajectories (orbits) |
| dc.subject.en | Asymptotics of solutions |
| dc.subject.en | Operator norm |
| dc.subject.en | Minimal modulus |
| dc.subject.en | Jacobi matrices (operators) |
| dc.subject.en | Spectral properties |
| dc.subject.en | Absolutely continuous spectrum |
| dc.title | Uni-asymptotic Linear systems and Jacobi Operators |
| dc.type | JournalArticle |
| dspace.entity.type | Publication |