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.
Bibliographical noteFunding 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.
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- Jacobi matrices
- Spectral theory