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arXiv · 1612.04051

Optimal Hardy inequalities for Schrödinger operators on graphs

Matthias Keller·Yehuda Pinchover·Felix Pogorzelski
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Abstract

For a given subcritical discrete Schrödinger operator $H$ on a weighted infinite graph $X$, we construct a Hardy-weight $w$ which is optimal in the following sense. The operator $H - λw$ is subcritical in $X$ for all $λ< 1$, null-critical in $X$ for $λ= 1$, and supercritical near any neighborhood of infinity in $X$ for any $λ> 1$. Our results rely on a criticality theory for Schrödinger operators on general weighted graphs.

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Matthias Keller, Yehuda Pinchover, Felix Pogorzelski. 2017-08-31. Optimal Hardy inequalities for Schrödinger operators on graphs. https://arxiv.org/abs/1612.04051

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