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arXiv · 1509.09077

Geometry of reproducing kernels in model spaces near the boundary

Anton Baranov·Andreas Hartmann·Karim Kellay
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Abstract

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 minimalsystems 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 kernelsexist near each Ahern--Clark point which is not an analyticity point for $\theta$, whileovercompleteness may occur only near the Ahern--Clark points of infinite orderand is equivalent to a "zero localization property". In this context the notion ofquasi-analyticity appears naturally, and as a by-product of our results we give conditions in thespirit of Ahern--Clark for the restriction of a model space to a radius to be a class ofquasi-analyticity.

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Anton Baranov, Andreas Hartmann, Karim Kellay. 2015-09-30. Geometry of reproducing kernels in model spaces near the boundary. https://arxiv.org/abs/1509.09077

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