Dispersion for Schrödinger operators on regular trees

Kaïs Ammari, Mostafa Sabri

Research output: Contribution to journalArticlepeer-review


We prove dispersive estimates for two models: the adjacency matrix on a discrete regular tree, and the Schrödinger equation on a metric regular tree with the same potential on each edge/vertex. The latter model can be thought of as an extension of the case of periodic Schrödinger operators on the real line. We establish a t- 3 / 2-decay for both models which is sharp, as we give the first-order asymptotics.

Original languageEnglish (US)
Article number56
JournalAnalysis and Mathematical Physics
Issue number2
StatePublished - Apr 2022


  • Dispersion
  • Graphs
  • Quantum graphs
  • Stationary phase
  • Trees

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics


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