The Mellin transform and spectral properties of toric varieties
Abstract
In this article we apply results of 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, zk, k ∈ d, in Bargmann space and prove an "upstairs" version of the spectral density theorem of BGU. We also obtain for the zk's, "upstairs" versions of the results of STZ on distribution laws for eigenstates on toric varieties.
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