Periodic Jacobi matrices on trees
Copyright policy )Periodic Jacobi matrices on trees
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.
appeared as Adv. Math. 379 (2020), 107241; this version includes an addendum
- Northwestern University United States
- Northwestern University United States
- Hebrew University of Jerusalem Israel
- Northeastern University United States
- California Institute of Technology United States
47B36, 47B15 20E08, Jacobi (tridiagonal) operators (matrices) and generalizations, trees, spectral theory, Trees, 004, 510, Functional Analysis (math.FA), Mathematics - Spectral Theory, Mathematics - Functional Analysis, singular continuous spectrum, Lists of open problems, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Hermitian and normal operators (spectral measures, functional calculus, etc.), Groups acting on trees, periodic Jacobi matrix, gap labeling theorem, Spectral theory, Spectral Theory (math.SP), Jacobi matrices
47B36, 47B15 20E08, Jacobi (tridiagonal) operators (matrices) and generalizations, trees, spectral theory, Trees, 004, 510, Functional Analysis (math.FA), Mathematics - Spectral Theory, Mathematics - Functional Analysis, singular continuous spectrum, Lists of open problems, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Hermitian and normal operators (spectral measures, functional calculus, etc.), Groups acting on trees, periodic Jacobi matrix, gap labeling theorem, Spectral theory, Spectral Theory (math.SP), Jacobi matrices
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