Inner functions and zero sets for ℓ^p_A

2018/02/13 by Raymond Cheng, Javad Mashreghi, Cheng, Raymond +3
Mathematics · #Holomorphic and Operator Theory #Advanced Banach Space Theory #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.1802.04646

Abstract

In this paper we characterize the zero sets of functions from ℓ^p_A (the analytic functions on the open unit disk D whose Taylor coefficients form an ℓ^p sequence) by developing a concept of an "inner function" modeled by Beurling's discussion of the Hilbert space ℓ²_A (the classical Hardy space). The zero set criterion is used to construct families of zero sets which are not covered by classical results. In particular, it is proved that when p > 2, there are zero sets for ℓ^p_A which are not Blaschke sequences.

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