Communications in Mathematical Physics

, Volume 359, Issue 1, pp 101–119 | Cite as

2 Bounded Variation and Absolutely Continuous Spectrum of Jacobi Matrices

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Abstract

We disprove a conjecture of Breuer–Last–Simon (Breuer et al. in Constr Approx 32(2):221–254, 2010) concerning the absolutely continuous spectrum of Jacobi matrices with coefficients that obey an ℓ2 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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© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institute of MathematicsThe Hebrew UniversityJerusalemIsrael
  2. 2.Department of MathematicsRice UniversityHoustonUSA

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