关于对数凹函数与测度的最大交集位置
On maximal intersection position for logarithmically concave functions and measures
AI总结：
本文为对数凹函数卷积引入最大交集位置，证明John型定理及恒等分解，并推广至偶对数凹测度。
摘要：
本文引入并研究了对数凹函数卷积的一种新位置，可视为Artstein-Avidan和Katzin（2018）及Artstein-Avidan和Putterman（2022）所引入和研究的凸体最大交集位置的函数类比。我们的主要结果是一对对数凹函数的最大交集位置的John型定理，包括相应的恒等分解。该主要结果在非常弱的函数假设下成立；特别是，所考虑的函数可能都具有无界支撑。作为我们结果的一个应用，我们为偶的$\log$-凹测度引入了一个John型位置。
英文摘要：
A new position is introduced and studied for the convolution of log-concave functions, which may be regarded as a functional analogue of the maximum intersection position of convex bodies introduced and studied by Artstein-Avidan and Katzin (2018) and Artstein-Avidan and Putterman (2022). Our main result is a John-type theorem for the maximal intersection position of a pair of log-concave functions, including the corresponding decomposition of the identity. The main result holds under very weak assumptions on the functions; in particular, the functions considered may both have unbounded supports. As an application of our results, we introduce a John-type position for even $\log$-concave measures.
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