### 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.

Original language | English |
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Title of host publication | Analysis on graphs and its applications |

Editors | Pavel Exner, Jonathan P. Keating, Peter Kutchment, Toshikazu Sunada, Alexander Teplyaev |

Pages | 337-354 |

Number of pages | 18 |

Volume | 77 |

Publication status | Published - 15 Nov 2008 |

### Publication series

Name | Proceedings of Symposia in Pure Mathematics |
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Publisher | American Mathematical Society |

Volume | 77 |

ISSN (Print) | 0082-0717 |

### Keywords

- integro-differential equation
- schrodinger-type operators
- metric trees
- discrete trees

## Cite this

Brown, B. M., Langer, M., & Schmidt, K. M. (2008). The HELP inequality on trees. In P. Exner, J. P. Keating, P. Kutchment, T. Sunada, & A. Teplyaev (Eds.),

*Analysis on graphs and its applications*(Vol. 77, pp. 337-354). (Proceedings of Symposia in Pure Mathematics; Vol. 77).