Szego kernel的漸近展開

Abstract

這篇文章主要是討論兩種不同方法推得一漸近展開，一個方法是使用偏微分方程，另一則是複幾何。我簡化、修改S. Zelditch和Z. Lu 在推得此漸近展開的證明。主要的目標是描述漸近展開的行為，像是它和流形間的關係，以及比較兩種方法。

Two methods about asymptotic expansion of sections are studied in this note. One is by PDE, the other is by complex geometry. I simplify and modify some proofs in the papers by S. Zelditch and Z. Lu. The main goal is to describe the behavior of the expansion such as how the expansion relates to the underlying manifold, and to compare these two different methods.