1996/09/30 by Pascal J. Thomas, Thomas, Pascal J.
Mathematics · #32 #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #math.CV #msc:32
paper · pdf · doi:10.48550/arxiv.math/9609201
arxiv created 1996/10/01 · openalex publication_date 1996/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose two possible definitions for the notion of a sampling sequence (or set) for Hardy spaces of the disk. The first one is inspired by recent work of Bruna, Nicolau, and Øyma about interpolating sequences in the same spaces, and it yields sampling sets which do not depend on the value of p and correspond to the result proved for bounded functions (p=∞) by Brown, Shields and Zeller. The second notion, while formally closer to the one used for weighted Bergman spaces, is shown to lead to trivial situations only, but raises a possibly interesting problem.