Poisson kernel expansions for Schrödinger operators on trees

Nalini Anantharaman, Mostafa Sabri

Research output: Contribution to journalArticlepeer-review


We study Schrödinger operators on trees and construct associated Poisson kernels, in analogy to the Laplacian on the unit disc. We show that in the absolutely continuous spectrum, the generalized eigenfunctions of the operator are generated by the Poisson kernel. We use this to define a “Fourier transform”, giving a Fourier inversion formula and a Plancherel formula, where the domain of integration runs over the energy parameter and the geometric boundary of the tree.

Original languageEnglish (US)
Pages (from-to)243-268
Number of pages26
JournalJournal of Spectral Theory
Issue number1
StatePublished - 2019


  • Generalized eigenfunctions
  • Poisson kernel
  • Schrödinger operator
  • Trees

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Geometry and Topology


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