This paper studies, by employing analytical tools, the small‐time behavior of the heat content for the Poisson kernel over the unit ball in ${\mathbb{R}}^d$, $d⩾2$ by working with its related set covariance function. As a result, we obtain a representation for the third term in the expansion of the heat content over the unit ball and provide the explicit form of this term in the particular cases $d=2$ and $d=3$.

中文翻译：

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欧氏空间中单位球上泊松核的热含量

本文通过使用分析工具研究了泊松核在单位球上的小时间行为。 ${\mathbb{[R}}^d$， $d⩾2$通过使用其相关的集合协方差函数。结果，我们获得了单位球上热含量扩展的第三项表示，并在特定情况下提供了该项的明确形式$d=2$ 和 $d=3$。