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Geometry of reproducing kernels in model spaces near the boundary
| hal.structure.identifier | Department of Mathematics and Mechanics | |
| dc.contributor.author | BARANOV, Anton | |
| 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 | KELLAY, Karim | |
| dc.date.created | 2015 | |
| dc.date.issued | 2017 | |
| dc.identifier.issn | 0022-247X | |
| dc.description.abstractEn | We study two geometric properties of reproducing kernels in model spaces $K_\theta$ where $\theta$ is an inner function in the disc: overcompleteness and existence of uniformly minimal systems of reproducing kernels which do not contain Riesz basic sequences. Both of these properties are related to the notion of the Ahern-Clark point. It is shown that ``uniformly minimal non-Riesz"$ $ sequences of reproducing kernels exist near each Ahern-Clark point which is not an analyticity point for $\theta$, while overcompleteness may occur only near the Ahern--Clark points of infinite order and is equivalent to a ``zero localization property". In this context the notion of quasi-analyticity appears naturally, and as a by-product of our results we give conditions in the spirit of Ahern--Clark for the restriction of a model space to a radius to be a class of quasi analyticity. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | minimal system | |
| dc.subject.en | uniform minimal system | |
| dc.subject.en | model space | |
| dc.subject.en | reproducing kernel | |
| dc.subject.en | Riesz sequence | |
| dc.subject.en | overcompleteness | |
| dc.subject.en | quasi-analyticity | |
| dc.title.en | Geometry of reproducing kernels in model spaces near the boundary | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 1509.09077 | |
| bordeaux.journal | Journal of Mathematical Analysis and Applications | |
| bordeaux.page | 971-987 | |
| bordeaux.volume | 447 | |
| bordeaux.issue | 2 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01206383 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01206383v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Mathematical%20Analysis%20and%20Applications&rft.date=2017&rft.volume=447&rft.issue=2&rft.spage=971-987&rft.epage=971-987&rft.eissn=0022-247X&rft.issn=0022-247X&rft.au=BARANOV,%20Anton&HARTMANN,%20Andreas&KELLAY,%20Karim&rft.genre=article |
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