Date of Award

Fall 12-2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics & Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

Raymond Cheng

Committee Member

Yet Nguyen

Committee Member

Richard D. Noren

Committee Member

David Selover

Committee Member

Xiang Xu

Abstract

Define ℓpA as the space of all functions holomorphic over the unit disk whose Taylor coefficients are p-summable. Despite their classical origins and simple definition, these spaces are not as well understood as one might expect. This is particularly true when compared with the Hardy spaces, which provide a useful road map for the types of questions we might consider reasonable. In this work we examine the zero sets of ℓpA, p ∈ (1;∞), as well as a notion of inner function that is consistent with the approach taken on numerous other function spaces. Basic properties of p-inner functions are proved. It is shown that for some values of p, there are Blaschke sequences that fail to be a zero set for ℓpA. It is also shown that canonical factorization fails for ℓpA .

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DOI

10.25777/1g5d-3p51

ISBN

9798780611837

ORCID

0000-0003-2026-0064

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