We investigate the Courrège theorem in the context of linear operators that satisfy the positive maximum principle on a space of continuous functions over a symmetric space. Applications are given to Feller–Markov processes. We also introduce Gangolli operators, which satisfy the positive maximum principle, and generalise the form associated with the generator of a Lévy process on a symmetric space. When the space is compact, we show that Gangolli operators are pseudo-differential operators having scalar symbols.

中文翻译：

---

对称空间上的正最大原理

我们在满足对称空间上连续函数空间上的正最大原理的线性算子的上下文中研究Courrège定理。应用程序适用于Feller–Markov过程。我们还介绍了满足正最大原理的Gangolli算子，并推广了对称空间上与Lévy过程的生成器相关的形式。当空间紧凑时，我们证明Gangolli算子是具有标量符号的伪微分算子。