Date Thesis Awarded
4-2019
Access Type
Honors Thesis -- Access Restricted On-Campus Only
Degree Name
Bachelors of Science (BS)
Department
Mathematics
Advisor
Pierre Clare
Committee Members
Vladimir Bolotnikov
Vassiliki Panoussi
Abstract
We recall a theory generalizing the Heisenberg group on $\R$ to an analogous structure using a locally compact abelian group $G$. Then, using our new, general Heisenberg groups, we generalize the classical Weil-Brezin map, from an operator on $L^2(\R )$ and develop a theory of that generalized Weil-Brezin map on $L^2(G)$ for some locally compact abelian group $G$. We then apply our generalized Weil-Brezin map to recover the Poisson Summation Formula as well as the Plancherel Theorem.
Recommended Citation
Bechtold, Benjamin, "A General Weil-Brezin Map and Some Applications" (2019). Undergraduate Honors Theses. William & Mary. Paper 1419.
https://scholarworks.wm.edu/honorstheses/1419
