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تسجيل مستخدم جديدGeometry of reproducing kernels in model spaces near the boundary
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Anton Baranov
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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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