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arXiv · 2310.11118

$L^p$ positivity preservation and self-adjointness on incomplete Riemannian manifolds

Andrea Bisterzo·Giona Veronelli
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Abstract

The aim of this paper is to prove a qualitative property, namely the preservation of positivity, for Schrödinger-type operators acting on $L^p$ functions defined on (possibly incomplete) Riemannian manifolds. A key assumption is a control of the behaviour of the potential of the operator near the Cauchy boundary of the manifolds. As a by-product, we establish the essential self-adjointness of such operators, as well as its generalization to the case $p\neq 2$, i.e. the fact that smooth compactly supported functions are an operator core for the Schrödinger operator in $L^p$.

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Andrea Bisterzo, Giona Veronelli. 2023-10-18. $L^p$ positivity preservation and self-adjointness on incomplete Riemannian manifolds. https://arxiv.org/abs/2310.11118

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