BARANOV, Anton; HARTMANN, Andreas; KELLAY, Karim

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BARANOV, Anton
Department of Mathematics and Mechanics

HARTMANN, Andreas
Institut de Mathématiques de Bordeaux [IMB]

KELLAY, Karim
Institut de Mathématiques de Bordeaux [IMB]

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Ce document a été publié dans

Journal of Mathematical Analysis and Applications. 2017, vol. 447, n° 2, p. 971-987

Elsevier

Résumé en anglais

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.< Réduire

Mots clés en anglais

minimal system

uniform minimal system

model space

reproducing kernel

Riesz sequence

overcompleteness

quasi-analyticity

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251