Periodic Jacobi matrices on trees

Nir Avni; Jonathan Breuer; Barry Simon

doi:10.1016/j.aim.2020.107241

Periodic Jacobi matrices on trees

Nir Avni, Jonathan Breuer, Barry Simon^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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.

Original language	English
Article number	107241
Journal	Advances in Mathematics
Volume	370
DOIs	https://doi.org/10.1016/j.aim.2020.107241
State	Published - 26 Aug 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Inc.

Keywords

Jacobi matrices
Spectral theory
Trees

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10.1016/j.aim.2020.107241

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title = "Periodic Jacobi matrices on trees",

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.",

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AB - 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.

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Periodic Jacobi matrices on trees

Abstract

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Keywords

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