${\ell }^2$ bounded variation and absolutely continuous spectrum of Jacobi matrices

Abstract

We disprove a conjecture of Breuer-Last-Simon concerning the absolutely continuous spectrum of Jacobi matrices with coefficients that obey an ${\ell }^2$ bounded variation condition with step $q$. We prove existence of a.c. spectrum on a smaller set than that specified by the conjecture and prove that our result is optimal.

21 pages

References in corpus (2)

• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operators
• On generalized sum rules for Jacobi matrices

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