Periodic Jacobi matrices on trees
Periodic Jacobi matrices on trees
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DOI：
10.1016/j.aim.2020.107241
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发表时间：
2019-11
影响因子：
1.7
通讯作者：
Nir Avni;Jonathan Breuer;B. Simon
中科院分区：
文献类型：
--
作者：
Nir Avni;Jonathan Breuer;B. Simon
本文开始系统地研究了树上周期Jacobi矩阵的谱理论，给出了其形式定义。这里首次出现的最重要的结果是这些算子没有奇异连续谱。我们回顾了Sunada和Aomoto以前的重要结果，并提出了几个有启发性的例子。我们提出了许多开放的问题和建议，我们希望将刺激进一步的工作。
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.