Optimal Hardy inequalities for Schr\"odinger operators on graphs

Matthias Keller; Yehuda Pinchover; Felix Pogorzelski

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arXiv · 1612.04051

Optimal Hardy inequalities for Schr\"odinger operators on graphs

Matthias Keller·Yehuda Pinchover·Felix Pogorzelski

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Abstract

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

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BibTeX RIS

Matthias Keller, Yehuda Pinchover, Felix Pogorzelski. 2016-12-13. Optimal Hardy inequalities for Schr\"odinger operators on graphs. https://arxiv.org/abs/1612.04051

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