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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2017

Geometry of reproducing kernels in model spaces near the boundary

Résumé

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.
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hal-01206383 , version 1 (28-09-2015)

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Anton Baranov, Andreas Hartmann, Karim Kellay. Geometry of reproducing kernels in model spaces near the boundary. Journal of Mathematical Analysis and Applications, 2017, 447 (2), pp.971-987. ⟨hal-01206383⟩

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