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

Yoram Last; Milivoje Lukic

doi:10.1007/s00220-017-3015-6

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arXiv · 1702.05245

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

Yoram Last·Milivoje Lukic

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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.

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BibTeX RIS

Yoram Last, Milivoje Lukic. 2017-02-17. $\ell^2$ bounded variation and absolutely continuous spectrum of Jacobi matrices. https://doi.org/10.1007/s00220-017-3015-6

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