论文标题
lie lie-malliavin定理的lie-malliavin定理
A Dixmier-Malliavin theorem for Lie groupoids
论文作者
论文摘要
Dixmier-Malliavin的著名定理断言，在谎言组上，每个平滑，紧凑的函数都可以表示为有限总和，其中每个项是卷积，相对于HAAR度量，具有两个这样的功能。我们确定li lie groupoid的同样存在。大部分繁重的举重是由dixmier-malliavin的原始工作中的引理完成的。我们还需要Lie代数的技术和指数图的相应概念。作为一种应用，我们在单位空间的不变子曼群上的函数消失并给定的序列中，在平滑卷积代数中的理想算术算术获得了结果。
A famous theorem of Dixmier-Malliavin asserts that every smooth, compactly-supported function on a Lie group can be expressed as a finite sum in which each term is the convolution, with respect to Haar measure, of two such functions. We establish that the same holds for a Lie groupoid. Most of the heavy lifting is done by a lemma in the original work of Dixmier-Malliavin. We also need the technology of Lie algebroids and the corresponding notion of exponential map. As an application, we obtain a result on the arithmetic of ideals in the smooth convolution algebra of a Lie groupoid arising from functions vanishing to given order on an invariant submanifold of the unit space.
