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ℓ 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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Author information

Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University, 9190401, Jerusalem, Israel

    Yoram Last

  2. Department of Mathematics, Rice University, Houston, TX, 77005, USA

    Milivoje Lukic

Authors
  1. Yoram Last
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  2. Milivoje Lukic
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Correspondence to Milivoje Lukic.

Additional information

Communicated by P. Deift

Y. Last: Supported in part by Grant No. 2014337 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.

M. Lukic: Supported in part by NSF Grant DMS-1301582.

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Last, Y., Lukic, M. ℓ 2 Bounded Variation and Absolutely Continuous Spectrum of Jacobi Matrices. Commun. Math. Phys. 359, 101–119 (2018). https://doi.org/10.1007/s00220-017-3015-6

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  • DOI: https://doi.org/10.1007/s00220-017-3015-6

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