Geometry of reproducing kernels in model spaces near the boundary

We study two geometric properties of reproducing kernels in model spaces Kθ where θ is an inner function: 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 θ, 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.