The HELP inequality on trees

B. Malcolm Brown, Matthias Langer, Karl Michael Schmidt

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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.
Original languageEnglish
Title of host publicationAnalysis on graphs and its applications
EditorsPavel Exner, Jonathan P. Keating, Peter Kutchment, Toshikazu Sunada, Alexander Teplyaev
Pages337-354
Number of pages18
Volume77
Publication statusPublished - 15 Nov 2008

Publication series

NameProceedings of Symposia in Pure Mathematics
PublisherAmerican Mathematical Society
Volume77
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).