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 \(\alpha \)-Hermite Bounded Variation and its functional capacity and geometrical perimeter.

中文翻译：

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来自$$ \ alpha $$α的容量和周长-铁矿的有界变化

令\（{\ mathcal {H}} _ {\ alpha} = \ Delta-（\ alpha -1）| x | ^ {\ alpha} \）为\（[1，\ infty）\ ni \ alpha \ ）-位于\（{\ mathbb {R}} ^ d \）中原点的氢原子的Hermite算子。在本文中，我们受经典情况\（\ alpha = 1 \）的启发，研究具有\（\ alpha \） - Hermite有界变化的函数的空间及其功能和几何周长。