Award Date
12-1-2020
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
First Committee Member
Zhijian Wu
Second Committee Member
Angel Muleshkov
Third Committee Member
Xin Li
Fourth Committee Member
Stephen Lepp
Number of Pages
86
Abstract
In this dissertation, we introduce a Nevanlinna-type counting function, $M_{\varphi, \alpha}$. We show that $M_{\varphi, \alpha}$ is subharmonic and continuous on $\theset$ by exhibiting certain properties of the logarithmic potential of the associated pullback measure of two-dimensional Lebesgue measure on $\mathbb{D}$. Different identities of $M_{\varphi, \alpha}$ are presented. A change-of-variable formula calculates precisely the weighted Bergman norms of composition functions in terms of $M_{\varphi, \alpha}$. Certain estimates involving $M_{\varphi, \alpha}$ and the associated pullback measure on Carleson windows and semi-disks are demonstrated. For weighted Bergman space $A^2_\alpha$, we characterize orthogonal self-maps and give the Hilbert Schmidt norm of $C_\varphi$.
Keywords
Distribution; Hardy space; Potential theory; Radial; Super harmonic; Weighted Bergman space
Disciplines
Mathematics
File Format
File Size
845 KB
Degree Grantor
University of Nevada, Las Vegas
Language
English
Repository Citation
Nguyen, John, "A Nevanlinna-Type Counting Function and Pullback Measure" (2020). UNLV Theses, Dissertations, Professional Papers, and Capstones. 4069.
http://dx.doi.org/10.34917/23469742
Rights
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