The Feichtinger conjecture for reproducing kernels in model subspaces

Abstract

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

14 pages

References in corpus (2)

• The Kadison-Singer Problem in Mathematics and Engineering
• Compact embeddings of model subspaces of the Hardy space