ℓ 2 Bounded Variation and Absolutely Continuous Spectrum of Jacobi Matrices

Yoram Last; Milivoje Lukic

doi:10.1007/s00220-017-3015-6

ℓ ² Bounded Variation and Absolutely Continuous Spectrum of Jacobi Matrices

Yoram Last
, Milivoje Lukic^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	101-119
Number of pages	19
Journal	Communications in Mathematical Physics
Volume	359
Issue number	1
DOIs	https://doi.org/10.1007/s00220-017-3015-6
State	Published - 1 Apr 2018

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© 2017, Springer-Verlag GmbH Germany.

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ℓ ² Bounded Variation and Absolutely Continuous Spectrum of Jacobi Matrices

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