Periodic Jacobi matrices on trees

Nir Avni, Jonathan Breuer, Barry Simon*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We begin the systematic study of the spectral theory of periodic Jacobi matrices on trees including a formal definition. The most significant result that appears here for the first time is that these operators have no singular continuous spectrum. We review important previous results of Sunada and Aomoto and present several illuminating examples. We present many open problems and conjectures that we hope will stimulate further work.

Original languageAmerican English
Article number107241
JournalAdvances in Mathematics
StatePublished - 26 Aug 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Inc.


  • Jacobi matrices
  • Spectral theory
  • Trees


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