Barrier nonsubordinacy and absolutely continuous spectrum of block Jacobi matrices

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 $d\ge 1$ and we give applications of our results to some concrete classes of block Jacobi matrices.

arXiv comment21 pages. The preprint arXiv:2301.00204v2 was split into two parts. This is the second part

References in corpus (5)

• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operators
• Periodic perturbations of unbounded Jacobi matrices II: Formulas for density
• Periodic perturbations of unbounded Jacobi matrices I: Asymptotics of generalized eigenvectors
• Spectral properties of block Jacobi matrices
• Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case II