Date of Graduation
5-2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics (PhD)
Degree Level
Graduate
Department
Mathematical Sciences
Advisor/Mentor
Andrew Raich
Committee Member
Phillip Harrington
Second Committee Member
Zachary Bradshaw
Keywords
Atomic Decomposition;Boundary Values in the Sense of Distributions;Hardy Spaces;Meta-Analytic Functions;Nonhomogeneous Cauchy-Riemann Equations;Schwarz Boundary Value Problem
Abstract
We prove that many of the boundary properties associated with functions in the classic holomorphic Hardy spaces on the complex unit disk are present in Hardy classes of solutions to certain nonhomogeneous Cauchy-Riemann equations and higher-order generalizations of these equations. Also, we explicitly solve generalizations of the Schwarz boundary value problem on the complex unit disk and the upper-half plane when the boundary condition is in terms of boundary values in the sense of distributions.
Citation
Blair, W. L. (2024). Generalizations of the Hardy Spaces and the Schwarz Boundary Value Problem. Graduate Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/5217
Included in
Atomic, Molecular and Optical Physics Commons, Control Theory Commons, Special Functions Commons