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A General Weil-Brezin Map and Some Applications

Bechtold, Benjamin
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.
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2019-04-01
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Undergraduate Honors Theses
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https://scholarworks.wm.edu/cgi/viewcontent.cgi?article=2432&context=honorstheses&unstamped=1
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Clare, Pierre
Bolotnikov, Vladimir
Panoussi, Vassiliki
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Mathematics
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https://scholarworks.wm.edu/handle/internal/10822
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