Thin sequences and their role in $H^p$ theory, model spaces, and uniform algebras

Abstract

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 $1\le p\le \infty$, providing several new ways to think about these sequences.