Barrier nonsubordinacy and absolutely continuous spectrum of block Jacobi matrices

2022/12/31 by Marcin Moszyński, Grzegorz Świderski, Moszyński, Marcin +1 · 1 citation
Materials Science · Mathematics · #47B36 (Primary) #FOS: Mathematics #Holomorphic and Operator Theory #Magnetism in coordination complexes #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2301.00204

openalex publication_date 2022/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explore to what extent the relation between the absolute continuous spectrum and non-existence of subordinate generalized eigenvectors, known for scalar Jacobi operators, can be formulated also for block Jacobi operators with d-dimensional blocks. The main object here allowing to make some progress in that direction is the new notion of the barrier nonsubordinacy. We prove that the barrier nonsubordinacy implies the absolute continuity for block Jacobi operators. Finally, we extend some well-known d=1 conditions guaranteeing the absolute continuity to d ≥ 1 and we give applications of our results to some concrete classes of block Jacobi matrices.

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