Periodic Jacobi Matrices on Trees
Spectral Theory
2020-07-24 v3 Classical Analysis and ODEs
Functional Analysis
Abstract
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.
Cite
@article{arxiv.1911.02612,
title = {Periodic Jacobi Matrices on Trees},
author = {Nir Avni and Jonathan Breuer and Barry Simon},
journal= {arXiv preprint arXiv:1911.02612},
year = {2020}
}
Comments
appeared as Adv. Math. 379 (2020), 107241; this version includes an addendum