Thin Sequences and Their Role in $H^p$ Theory, Model Spaces, and Uniform Algebras

In this paper we revisit some facts about thin interpolating sequences in the unit disc from three perspectives: uniform algebras, model spaces, and $H^p$ spaces. We extend the notion of asymptotic interpolation to $H^p$ spaces, for $1\le p\le \mathrm{\infty }$, providing several new ways to think about these sequences.