Asymptotics for Bergman projections with smooth weights: a direct approach

Abstract

We extend the direct approach to the semiclassical Bergman kernel asymptotics, developed recently in Deleporte et al. (Ann Fac Sci Toulouse Math, 2020) for real analytic exponential weights, to the smooth case. Similar to Deleporte et al. (2020), 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.