Thin Sequences and Their Role in Model Spaces and Douglas Algebras
Journal of Fourier Analysis and Applications
We study thin interpolating sequences (z_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 (z _n) tends to 0. The interpolation properties in H^2 are essentially the same as those in K_Theta.
Gorkin, Pamela and Wick, Brett. "Thin Sequences and Their Role in Model Spaces and Douglas Algebras." Journal of Fourier Analysis and Applications 22, no. 1 (2016) : 137-158.