A construction of a pseudo-differential operator on non-archimedean local fields invariant under a finite group action is given together with the solution of the corresponding Cauchy problem. This construction is applied to parts of the Gerritzen-Herrlich Teichm\"uller space in order to obtain a self-adjoint operator whose spectrum can decide about certain properties of the reduction graph of the corresponding Mumford curves.

中文翻译：

---

p-Adic Mumford曲线模空间上的广义扩散

给出了有限群作用下非阿基米德局部场不变的伪微分算子的构造，并给出了相应的柯西问题的解。将该构造应用于 Gerritzen-Herrlich Teichm\"uller 空间的部分以获得自伴随算子，其频谱可以决定相应 Mumford 曲线的约简图的某些属性。