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Periodic Jacobi Matrices on Trees

Avni, Nir and Breuer, Jonathan and Simon, Barry (2020) Periodic Jacobi Matrices on Trees. Advances in Mathematics, 370 . Art. No. 107241. ISSN 0001-8708. https://resolver.caltech.edu/CaltechAUTHORS:20200108-134956957

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.aim.2020.107241DOIArticle
https://arxiv.org/abs/1911.02612arXivDiscussion Paper
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 2020 Elsevier Inc. 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.
Funders:
Funding AgencyGrant Number
NSFDMS-1902041
Binational Science Foundation (USA-Israel)2014337
Israel Science Foundation399/16
NSFDMS-1665526
Subject Keywords:Jacobi matrices; Trees; Spectral theory
Classification Code:2010 Mathematics Subject Classification: 47B36, 47B15, 20E08
Record Number:CaltechAUTHORS:20200108-134956957
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200108-134956957
Official Citation:Nir Avni, Jonathan Breuer, Barry Simon, Periodic Jacobi matrices on trees, Advances in Mathematics, Volume 370, 2020, 107241, ISSN 0001-8708, https://doi.org/10.1016/j.aim.2020.107241. (http://www.sciencedirect.com/science/article/pii/S000187082030267X)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100564
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Jan 2020 22:40
Last Modified:27 May 2020 21:20

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