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arXiv · 2403.14157

Semiclassical asymptotics for Bergman projections with Gevrey weights

Haoren Xiong·Hang Xu
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Abstract

We extend the direct approach to the semiclassical asymptotics for Bergman projections, developed by Deleporte--Hitrik--Sj\"ostrand for real analytic exponential weights and Hitrik--Stone for smooth exponential weights, to the case of Gevrey weights. We prove that the amplitude of the asymptotic Bergman projection forms a Gevrey symbol whose asymptotic coefficients obey certain Gevrey-type growth rate, and it is constructed by an asymptotic inversion of an explicit Fourier integral operator up to a Gevrey-type small remainder.

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Haoren Xiong, Hang Xu. 2024-03-21. Semiclassical asymptotics for Bergman projections with Gevrey weights. https://arxiv.org/abs/2403.14157

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