Separation of singularities for the Bergman space and application to control theory
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | HARTMANN, Andreas | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ORSONI, Marcu-Antone | |
| dc.date.accessioned | 2024-04-04T02:46:44Z | |
| dc.date.available | 2024-04-04T02:46:44Z | |
| dc.date.issued | 2021 | |
| dc.identifier.issn | 0021-7824 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191581 | |
| dc.description.abstractEn | In this paper, we solve a separation of singularities problem in the Bergman space. More precisely, we show that if $P\subset \mathbb{C}$ is a convex polygon which is the intersection of $n$ half planes, then the Bergman space on $P$ decomposes into the sum of the Bergman spaces on these half planes. The result applies to the characterization of the reachable space of the one-dimensional heat equation on a finite interval with boundary controls. We prove that this space is a Bergman space of the square which has the given interval as a diagonal. This gives an affirmative answer to a conjecture raised in [HKT20]. | |
| dc.description.sponsorship | Méthodes variationnelles pour les signaux sur graphe - ANR-18-CE40-0005 | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.title.en | Separation of singularities for the Bergman space and application to control theory | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.matpur.2021.04.009 | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Optimisation et contrôle [math.OC] | |
| dc.identifier.arxiv | 2104.05268 | |
| bordeaux.journal | Journal de Mathématiques Pures et Appliquées | |
| bordeaux.page | 181-201 | |
| bordeaux.volume | 150 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03194639 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03194639v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20de%20Math%C3%A9matiques%20Pures%20et%20Appliqu%C3%A9es&rft.date=2021&rft.volume=150&rft.spage=181-201&rft.epage=181-201&rft.eissn=0021-7824&rft.issn=0021-7824&rft.au=HARTMANN,%20Andreas&ORSONI,%20Marcu-Antone&rft.genre=article |
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