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

Pamela Gorkin; Sandra Pott; Brett D. Wick

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arXiv · 1312.5759

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

Pamela Gorkin·Sandra Pott·Brett D. Wick

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

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Pamela Gorkin, Sandra Pott, Brett D. Wick. 2013-12-19. Thin Sequences and Their Role in $H^p$ Theory, Model Spaces, and Uniform Algebras. https://arxiv.org/abs/1312.5759

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