Abstract
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 \(\Theta (\lambda _n) \rightarrow 0\) the interpolation properties in \(H^2\) are essentially the same as those in \(K_\Theta \).
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Pamela Gorkin Research supported in part by Simons Foundation Grant 243653. Brett D. Wick Research supported in part by a National Science Foundation DMS Grant # 0955432.
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Communicated by Yura Lyubarskii.
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Gorkin, P., Wick, B.D. Thin Sequences and Their Role in Model Spaces and Douglas Algebras. J Fourier Anal Appl 22, 137–158 (2016). https://doi.org/10.1007/s00041-015-9414-1
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DOI: https://doi.org/10.1007/s00041-015-9414-1