Date of Award
Doctor of Philosophy (PhD)
Mathematics & Statistics
Computational and Applied Mathematics
Richard D. Noren
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 .
Dragas, James G..
"On the p-Inner Functions of ℓpA"
(2021). Doctor of Philosophy (PhD), Dissertation, Mathematics & Statistics, Old Dominion University, DOI: 10.25777/1g5d-3p51