Geometry of reproducing kernels in model spaces near the boundary

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:447

Article

Baranov, A.¹  Hartmann, A.²  Kellay, K.² 

[1] St Petersburg State Univ, Dept Math & Mech, St Petersburg, Russia

[2] Univ Bordeaux, IMB, 351 Cours Liberat, F-33405 Talence, France

关键词: Model space;    Reproducing kernel;    Riesz sequence;    Uniformly minimal system;    Overcompleteness;    Quasi-analyticity;   

DOI  :  10.1016/j.jmaa.2016.10.007

来源: Elsevier

【 摘 要 】

We study two geometric properties of reproducing kernels in model spaces K-theta where theta 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 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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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