Date of Award
1-1-2015
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
College/School/Department
Department of Mathematics and Statistics
Content Description
1 online resource (v, 50 pages) : illustrations.
Dissertation/Thesis Chair
Rongwei Yang
Committee Members
Joshua Isralowitz, Michael Stessin, Rongwei Yang, Kehe Zhu
Keywords
Hardy space over bidisc, numerical invariants, operator model theory, operator pairs, submodule, Hardy spaces, Operator theory, Invariants
Subject Categories
Physical Sciences and Mathematics
Abstract
This thesis studies the submodules of $H^2(\mathbb{D}^2)$ by using operator theoretic approaches. The first part focus on the two pairs of operators (R_z,R_w) and (S_z,S_w) on a submodule. The second part studies the two-inner-sequences-based submodules from the point view of operator model theory. Lastly, using inner-sequence-based submodules, we show that the multivariable Berger-Shaw theorem may not exist.
Recommended Citation
Yang, Yixin, "On numerical invariants of submodules in H²(D²)" (2015). Legacy Theses & Dissertations (2009 - 2024). 1545.
https://scholarsarchive.library.albany.edu/legacy-etd/1545