On the heat content for the poisson kernels over the unit ball in the euclidean space

Abstract

This paper studies, by employing analytical tools, the small time behavior of the heat content for the Poisson kernel over the unit ball in $\Rd$, $d\ge 2$ 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 $d=3$.

References in corpus (3)

• Heat content for convolution semigroups
• Spectral Heat Content for Lévy Processes
• On the heat content of a polygon

Cited by in corpus (1)

• Heat content estimates for the fractional Schrödinger operator $\F+\ind$