The Feichtinger Conjecture for Reproducing Kernels

@inproceedings{Baranov2009TheFC,
title={The Feichtinger Conjecture for Reproducing Kernels},
author={Anton V. Baranov and Konstantin M. Dyakonov},
year={2009}
}

We obtain two results concerning the Feichtinger conjecture for systems of normalized reproducing kernels in the model subspace KΘ = H 2 ⊖ ΘH of the Hardy space H, where Θ is an inner function. First, we verify the Feichtinger conjecture for the kernels k̃λn = kλn/‖kλn‖ under the assumption that sup n |Θ(λn)| < 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)| < ε} is connected for some ε ∈ (0, 1).