The Mellin Transform and Spectral Properties of Toric Varieties |
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Authors: | Victor Guillemin Zuoqin Wang |
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Affiliation: | 1. Department of Mathematics, MIT, Cambridge, MA, 02139, USA
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Abstract: | In this paper we apply the 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, z k , $ k in mathbb{Z}^{d} $ , in Bargmann space and prove an “upstairs” version of the spectral density theorem of [BGU]. We also obtain for the z k ’s, “upstairs” versions of the results of [STZ] on distribution laws for eigenstates on toric varieties. |
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