The spectral density function for the Laplacian on high tensor powers of a line bundle
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 GuilleminUribe showed that there is a welldefined cluster of lowlying 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2001
 arXiv:
 arXiv:math/0103062
 Bibcode:
 2001math......3062B
 Keywords:

 Mathematics  Spectral Theory;
 Mathematics  Differential Geometry
 EPrint:
 AMSLatex, 17 pages