Thin Sequences and Their Role in Model Spaces and Douglas Algebras

We study thin interpolating sequences $\{λ_n\}$ and their relationship to interpolation in the Hardy space $H^2$ and the model spaces $K_Θ= H^2 \ominus ΘH^2$, where $Θ$ is an inner function. Our results, phrased in terms of the functions that do the interpolation as well as Carleson measures, show that under the assumption that $Θ(λ_n) \to 0$ the interpolation properties in $H^2$ are essentially the same as those in $K_Θ$.

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