We extend a classical theorem of Courrège to Lie groups in a global setting, thus characterising all linear operators on the space of smooth functions of compact support that satisfy the positive maximum principle. We show that these are Lévy type operators (with variable characteristics), and pseudo‐differential operators when the group is compact. If the characteristics are constant, then the operator is the generator of the contraction semigroup associated to a convolution semigroup of sub‐probability measures.

中文翻译：

---

李群的最大积极原则

我们将Courrège的经典定理扩展到全局条件下的Lie群，从而在满足正最大原理的紧支撑的光滑函数空间上表征所有线性算子。我们证明它们是Lévy型算子（具有可变特征），并且在组紧凑时是伪微分算子。如果特征是恒定的，则算子是与子概率测度的卷积半群相关联的收缩半群的生成者。