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The HELP inequality on trees

Brown, B. Malcolm and Langer, Matthias and Schmidt, Karl Michael (2008) The HELP inequality on trees. In: Analysis on graphs and its applications. Proceedings of Symposia in Pure Mathematics, 77 . American Mathematical Society, pp. 337-354. ISBN 0821844717

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Abstract

We establish analogues of Hardy and Littlewood's integro-differential equation for Schrödinger-type operators on metric and discrete trees, based on a generalised strong limit-point property of the graph Laplacian.