Capacity & Perimeter from $\alpha$-Hermite Bounded Variation

Abstract

Let ${\mathcal{H}}_{\alpha }=\Delta -(\alpha -1)|x{|}^{\alpha }$ be an $[1,\infty )\ni \alpha$-Hermite operator for the hydrogen atom located at the origin in ${\mathbb{R}}^d$. In this paper, we are motivated by the classical case $\alpha =1$ to investigate the space of functions with $\alpha$-{\it Hermite Bounded Variation} and its functional capacity and geometrical perimeter.

36 pages