关于熵功率不等式的可逆性问题
On the problem of reversibility of the entropy power inequality
AI总结：
本文研究熵功率不等式的可逆性问题，证明凸概率分布类整体不满足可逆性，同时探讨了同分布加项的相关现象，完善了熵功率不等式可逆性的适用范围结论。
摘要：
作者近期研究表明，当独立加项的分布处于特殊位置且密度函数具有充分凹性时，熵功率不等式是可逆的。本注记证明，在整个凸概率分布类上，该可逆性并不成立。文中还讨论了同分布加项的相关现象。
英文摘要：
As was shown recently by the authors, the entropy power inequality can be reversed for independent summands with sufficiently concave densities, when the distributions of the summands are put in a special position. In this note it is proved that reversibility is impossible over the whole class of convex probability distributions. Related phenomena for identically distributed summands are also discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
