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arXiv · 0906.2158

The Feichtinger conjecture for reproducing kernels in model subspaces

Anton Baranov·Konstantin Dyakonov
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Abstract

We obtain two results concerning the Feichtinger conjecture for systems of normalized reproducing kernels in the model subspace $K_Θ= H^2\ominus ΘH^2$ of the Hardy space $H^2$, where $Θ$ is an inner function. First, we verify the Feichtinger conjecture for the kernels $ \tilde k_{λ_n} = k_{λ_n}/\|k_{λ_n}\|$ under the assumption that $\sup_n |Θ(λ_n)|<1$. Secondly, we prove the Feichtinger conjecture in the case where $Θ$ is a one-component inner function, meaning that the set $\{z:|Θ(z)|<\varepsilon\}$ is connected for some $\varepsilon\in(0,1)$.

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Anton Baranov, Konstantin Dyakonov. 2009-06-11. The Feichtinger conjecture for reproducing kernels in model subspaces. https://arxiv.org/abs/0906.2158

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