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arXiv · 1911.02612

Periodic Jacobi Matrices on Trees

Nir Avni·Jonathan Breuer·Barry Simon
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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.

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Nir Avni, Jonathan Breuer, Barry Simon. 2019-11-06. Periodic Jacobi Matrices on Trees. https://arxiv.org/abs/1911.02612

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