Thin Sequences and Their Role in Model Spaces and Douglas Algebras

We study thin interpolating sequences ${lambda_n}$ and their relationship to interpolation in the Hardy space $H^2$ and the model spaces $K_Theta = H^2 ominus Theta H^2$, where $Theta$ 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 $Theta(lambda_n) to 0$ the interpolation properties in $H^2$ are essentially the same as those in $K_Theta$.