Asymptotics for Bergman projections with smooth weights: a direct approach
Complex Variables
2021-06-01 v1 Analysis of PDEs
Functional Analysis
Abstract
We adapt the direct approach to the semiclassical Bergman kernel asymptotics, developed recently by A. Deleporte, J. Sj\"ostrand, and the first-named author for real analytic exponential weights, to the smooth case. Similar to that work, our approach avoids the use of the Kuranishi trick and it allows us to construct the amplitude of the asymptotic Bergman projection by means of an asymptotic inversion of an explicit Fourier integral operator.
Keywords
Cite
@article{arxiv.2105.14402,
title = {Asymptotics for Bergman projections with smooth weights: a direct approach},
author = {Michael Hitrik and Matthew Stone},
journal= {arXiv preprint arXiv:2105.14402},
year = {2021}
}