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.