Free regular convolution semigroups describe the distribution of free subordinators, while Bondesson class convolution semigroups correspond to classical subordinators with completely monotone Lévy density. We show that these two classes of convolution semigroups are in bijection with the class of complete Bernstein functions, and we establish an integral identity linking the two semigroups. We provide several explicit examples that illustrate this result.

中文翻译：

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关于自由正则和 Bondesson 卷积半群

自由正则卷积半群描述自由从属子的分布，而邦德森类卷积半群对应于完全单调 Lévy 密度的经典从属子。我们证明这两类卷积半群与完全 Bernstein 函数类是双射的，并且我们建立了连接这两个半群的积分恒等式。我们提供了几个明确的例子来说明这个结果。