与广义熵及模群相关的一个函数方程
经典分析与常微分方程
2020-03-05 v2 概率论
摘要
我们求解了一个与广义信息函数的代数刻画相关的函数方程。为证明解的对称性,我们研究了一个涉及两个单应变换的相关函数方程组。这些变换生成模群,这一事实在求解该方程组中起着关键作用。该方法暗示了条件概率与算术之间更一般的关系。
引用
@article{arxiv.1910.06927,
title = {A functional equation related to generalized entropies and the modular group},
author = {Daniel Bennequin and Juan Pablo Vigneaux},
journal= {arXiv preprint arXiv:1910.06927},
year = {2020}
}
备注
Originally uploaded as an appendix to arXiv:1709.07807v1. Changes in v2: the introduction was extended to summarize in more detail previous results; there is a new lemma at the end of Section 4