论文标题
单位圆和叶子连锁店上的添加过程
Additive processes on the unit circle and Loewner chains
论文作者
论文摘要
本文定义了一类减少径向洛瓦纳链的发电机概念，这些链条仅相对于时间是连续的。为此，定义和分析了Loewner的微分方程的“ Loewner的积分方程”。发电机的定义是由Lévy-khintchine表示单位圆上的加法过程的动机。实际上，我们可以并且确实可以在上述LOEWNER链条和配备合适拓扑的加法过程的增量分布之间引入同态形态。另一方面，从非共同概率理论的角度来看，上述发电机还诱导了具有其他物体的射击：尤其是单调卷积半流和自由卷积半流。最后，计算由从从属的自由卷积半流构建的Loewner链的发电机。
This paper defines the notion of generators for a class of decreasing radial Loewner chains which are only continuous with respect to time. For this purpose, "Loewner's integral equation" which generalizes Loewner's differential equation is defined and analyzed. The definition of generators is motivated by the Lévy-Khintchine representation for additive processes on the unit circle. Actually, we can and do introduce a homeomorphism between the above class of Loewner chains and the set of the distributions of increments of additive processes equipped with suitable topologies. On the other hand, from the viewpoint of non-commutative probability theory, the above generators also induce bijections with some other objects: in particular, monotone convolution hemigroups and free convolution hemigroups. Finally, the generators of Loewner chains constructed from free convolution hemigroups via subordination are computed.
