Revista Matemática Iberoamericana


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Volume 31, Issue 3, 2015, pp. 841–864
DOI: 10.4171/RMI/856

Published online: 2015-10-29

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

Pamela Gorkin[1], Sandra Pott[2] and Brett D. Wick[3]

(1) Bucknell University, Lewisburg, USA
(2) Lund University, Sweden
(3) Georgia Institute of Technology, Atlanta, USA

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

Keywords: Hardy space, thin sequences, interpolation, asymptotic orthonormal sequence

Gorkin Pamela, Pott Sandra, Wick Brett: Thin sequences and their role in $H^p$ theory, model spaces, and uniform algebras. Rev. Mat. Iberoamericana 31 (2015), 841-864. doi: 10.4171/RMI/856