The local limit theorem on nilpotent Lie groups
The local limit theorem on nilpotent Lie groups
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DOI：
10.1007/s00440-018-0864-7
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发表时间：
2018-01
影响因子：
2
通讯作者：
Robert D. Hough
中科院分区：
文献类型：
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作者：
Robert D. Hough
对于一类满足矩条件和阿贝尔化特征函数条件的生成测度，在连通、单连通幂零李群上证明了一个局部极限定理.这一结果推广了早期的局部极限定理的Alexopoulos治疗绝对连续措施的连续密度的紧支持，也推广了局部极限定理的Breuillard和Diaconis-Hough治疗一般措施的海森堡群。
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 theorem 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.