Communications in Mathematical Physics

, Volume 358, Issue 2, pp 767–790 | Cite as

Optimal Hardy inequalities for Schrödinger operators on graphs

  • Matthias Keller
  • Yehuda Pinchover
  • Felix Pogorzelski


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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Authors and Affiliations

  1. 1.Institut für MathematikUniversität PotsdamPotsdamGermany
  2. 2.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael
  3. 3.Institut für MathematikUniversität LeipzigLeipzigGermany

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