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arXiv · 0706.3696

The Mellin transform and spectral properties of toric varieties

Victor Guillemin·Zuoqin Wang
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Abstract

In this article we apply results of \cite{W} on the twisted Mellin transform to problems in toric geometry. In particular we use these results to describe the asymptotics of probability densities associated with the monomial eigenstates, $z^k$, $k \in \ZZ^d$, in Bargmann space and prove an "upstairs" version of the spectral density theorem of \cite{BGU}. We also obtain for the $z^k$'s, "upstairs" versions of the results of \cite{STZ} on distribution laws for eigenstates on toric varieties.

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Victor Guillemin, Zuoqin Wang. 2007-06-27. The Mellin transform and spectral properties of toric varieties. https://arxiv.org/abs/0706.3696

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