幂零李群上的局部极限定理
The local limit theorem on nilpotent Lie groups
摘要：
在连通、单连通幂零李群上，对一类满足矩条件和阿贝尔化的特征函数条件的生成测度，证明了一个局部极限定理.这一结果推广了Alexopoulos的一个较早的局部极限定理，该定理处理了具有连续紧支集密度的绝对连续测度，也推广了Breuillard和Diaconis-Hough的局部极限定理，该定理处理了Heisenberg群上的一般测度.
英文摘要：
A local limit theorem is proven on connected, simply connected nilpotent Lie groups, for a class of generating measures satisfying a moment condition and a condition on the characteristic function of the abelianization. The result extends an earlier local limit theorems of Alexopoulos which treated absolutely continuous measures with a continuous density of compact support, and also extends local limit theorems of Breuillard and Diaconis-Hough which treated general measures on the Heisenberg group.
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