This paper studies, by employing analytical tools, the small time behavior of the heat content for the Poisson kernel over the unit ball in $\Rd$, $d\geq 2$ 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 the this term in the particular cases $d=2$ and $d=3$.
Categories: math.PR