The Spectral Density Function for the Laplacian on High Tensor Powers of a Line Bundle |
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Authors: | David Borthwick Alejandro Uribe |
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Affiliation: | (1) Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, U.S.A.;(2) Mathematics Department, University of Michigan, Ann Arbor, MI, 48109, U.S.A. |
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Abstract: | For a symplectic manifold with quantizing line bundle, a choice of almost complex structure determines a Laplacian acting on tensor powers of the bundle. For high tensor powers Guillemin–Uribe showed that there is a well-defined cluster of low-lying eigenvalues, whose distribution is described by a spectral density function. We give an explicit computation of the spectral density function, by constructing certain quasimodes on the associated principle bundle. |
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Keywords: | almost Kä hler spectral density function quasimode |
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