The HELP inequality on trees

B. Malcolm Brown, Matthias Langer, Karl Michael Schmidt

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

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.
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

Fingerprint

Graph Laplacian
Limit Point
Schrödinger
Integro-differential Equation
Analogue
Metric
Operator

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).
Brown, B. Malcolm ; Langer, Matthias ; Schmidt, Karl Michael. / The HELP inequality on trees. Analysis on graphs and its applications. editor / Pavel Exner ; Jonathan P. Keating ; Peter Kutchment ; Toshikazu Sunada ; Alexander Teplyaev. Vol. 77 2008. pp. 337-354 (Proceedings of Symposia in Pure Mathematics).
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Brown, BM, Langer, M & Schmidt, KM 2008, The HELP inequality on trees. in P Exner, JP Keating, P Kutchment, T Sunada & A Teplyaev (eds), Analysis on graphs and its applications. vol. 77, Proceedings of Symposia in Pure Mathematics, vol. 77, pp. 337-354.

The HELP inequality on trees. / Brown, B. Malcolm; Langer, Matthias; Schmidt, Karl Michael.

Analysis on graphs and its applications. ed. / Pavel Exner; Jonathan P. Keating; Peter Kutchment; Toshikazu Sunada; Alexander Teplyaev. Vol. 77 2008. p. 337-354 (Proceedings of Symposia in Pure Mathematics; Vol. 77).

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

TY - CHAP

T1 - The HELP inequality on trees

AU - Brown, B. Malcolm

AU - Langer, Matthias

AU - Schmidt, Karl Michael

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N2 - 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.

AB - 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.

KW - integro-differential equation

KW - schrodinger-type operators

KW - metric trees

KW - discrete trees

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M3 - Chapter (peer-reviewed)

SN - 0821844717

VL - 77

T3 - Proceedings of Symposia in Pure Mathematics

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EP - 354

BT - Analysis on graphs and its applications

A2 - Exner, Pavel

A2 - Keating, Jonathan P.

A2 - Kutchment, Peter

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Brown BM, Langer M, Schmidt KM. The HELP inequality on trees. In Exner P, Keating JP, Kutchment P, Sunada T, Teplyaev A, editors, Analysis on graphs and its applications. Vol. 77. 2008. p. 337-354. (Proceedings of Symposia in Pure Mathematics).