Optimal Hardy inequalities for Schrödinger operators on graphs

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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Correspondence to Felix Pogorzelski.

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Communicated by R. Seiringer

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Keller, M., Pinchover, Y. & Pogorzelski, F. Optimal Hardy inequalities for Schrödinger operators on graphs. Commun. Math. Phys. 358, 767–790 (2018). https://doi.org/10.1007/s00220-018-3107-y

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