Periodic Jacobi matrices on trees

Nir Avni; Jonathan Breuer; Barry Simon

doi:https://doi.org/10.1016/j.aim.2020.107241

Periodic Jacobi matrices on trees

Nir Avni, Jonathan Breuer, Barry Simon

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

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

Keywords

Jacobi matrices
Spectral theory
Trees

All Science Journal Classification (ASJC) codes

General Mathematics

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https://doi.org/10.1016/j.aim.2020.107241

Cite this

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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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year = "2020",

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doi = "https://doi.org/10.1016/j.aim.2020.107241",

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AU - Avni, Nir

AU - Breuer, Jonathan

AU - Simon, Barry

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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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KW - Spectral theory

KW - Trees

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U2 - https://doi.org/10.1016/j.aim.2020.107241

DO - https://doi.org/10.1016/j.aim.2020.107241

M3 - مقالة

SN - 0001-8708

VL - 370

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 107241

ER -

Periodic Jacobi matrices on trees

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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