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

10 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	American 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

Funding Information:
Research supported in part by NSF grant DMS-1902041.Research supported in part by Israeli BSF Grant No. 2014337. and Israel Science Foundation Grant No. 399/16.Research supported in part by NSF grant DMS-1665526 and in part by Israeli BSF Grant No. 2014337.

Publisher Copyright:
© 2020 Elsevier Inc.

Keywords

Jacobi matrices
Spectral theory
Trees

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10.1016/j.aim.2020.107241

Cite this

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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.",

keywords = "Jacobi matrices, Spectral theory, Trees",

author = "Nir Avni and Jonathan Breuer and Barry Simon",

note = "Funding Information: Research supported in part by NSF grant DMS-1902041.Research supported in part by Israeli BSF Grant No. 2014337. and Israel Science Foundation Grant No. 399/16.Research supported in part by NSF grant DMS-1665526 and in part by Israeli BSF Grant No. 2014337. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

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AU - Breuer, Jonathan

AU - Simon, Barry

N1 - Funding Information: Research supported in part by NSF grant DMS-1902041.Research supported in part by Israeli BSF Grant No. 2014337. and Israel Science Foundation Grant No. 399/16.Research supported in part by NSF grant DMS-1665526 and in part by Israeli BSF Grant No. 2014337. Publisher Copyright: © 2020 Elsevier Inc.

PY - 2020/8/26

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N2 - 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.

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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DO - 10.1016/j.aim.2020.107241

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VL - 370

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ER -

Periodic Jacobi matrices on trees

Abstract

Bibliographical note

Keywords

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