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arXiv · 2104.11689

Inversion formulae for Siegel transforms

Mishel Skenderi
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Abstract

Let $n \in \mathbb{Z}_{\geq 3}$ be given. We prove Lebesgue-almost everywhere pointwise inversion formulae for the Siegel transforms in the geometry of numbers. These inversion formulae are quite general; for instance, they are valid for the Siegel transforms of any even and compactly supported Borel measurable function $f : \mathbb{R}^n \to \mathbb{R}$ that belongs to $L^1(\mathbb{R}^n) \cap L^2(\mathbb{R}^n).$

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Mishel Skenderi. 2022-06-16. Inversion formulae for Siegel transforms. https://arxiv.org/abs/2104.11689

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