This article is a continuation of a series by the authors on partial Bergman kernels and their asymptotic expasions. We prove a 2-term pointwise Weyl law for semi-classical spectral projections onto sums of eigenspaces of spectral width ħ = k -1 of Toeplitz quantizations (Formula presented) of Hamiltonians on powers L k of a positive Hermitian holomorphic line bundle L → M over a Kähler manifold. The first result is a complete asymptotic expansion for smoothed spectral projections in terms of periodic orbit data. When the orbit is ‘strongly hyperbolic’ the leading coefficient defines a uniformly continuous measure on R and a semi-classical Tauberian theorem implies the 2-term expansion. As in previous works in the series, we use scaling asymptotics of the Boutet-de-Monvel–Sjostrand parametrix and Taylor expansions to reduce the proof to the Bargmann–Fock case.
CITATION STYLE
Zelditch, S., & Zhou, P. (2018). Pointwise weyl law for partial bergman kernels. In Springer Proceedings in Mathematics and Statistics (Vol. 269, pp. 589–634). Springer New York LLC. https://doi.org/10.1007/978-3-030-01588-6_13
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