论文标题
伪差异操作员及其符号的等效性通过čech-dolbeault的共同学
The equivalence of pseudodifferential operators and their symbols via Čech-Dolbeault cohomology
论文作者
论文摘要
在本文中，我们构建了从伪差异操作员到其符号类别的捆式形态。由于该地图很难直接构建，因此我们用两个原始想法实现了这一点。首先，为了计算共同体，我们使用本田，Izawa和Suwa引入的Čech-Dolbeault共同体理论。其次，我们构建了一个新的符号类，该类称为$ c^\ infty $ -type的符号。这些想法使我们能够构建捆式形态，这实际上是滑轮的同构。
In this paper we construct the sheaf morphism from the sheaf of pseudodifferential operators to its symbol class. Since the map is hard to construct directly, we realize it with two original ideas as follows. First, to calculate cohomologies we use the theory of Čech-Dolbeault cohomology introduced by Honda, Izawa and Suwa. Secondly we construct a new symbol class, which is called the symbols of $C^\infty$-type. These ideas enable us to construct the sheaf morphism, which is actually an isomorphism of sheaves.
