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Geometry of reproducing kernels in model spaces near the boundary
Language
en
Article de revue
This item was published in
Journal of Mathematical Analysis and Applications. 2017, vol. 447, n° 2, p. 971-987
Elsevier
English 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 minimal systems of reproducing kernels which ...Read more >
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.Read less <
English Keywords
minimal system
uniform minimal system
model space
reproducing kernel
Riesz sequence
overcompleteness
quasi-analyticity
Origin
Hal imported