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

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

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

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-017-3015-6

Cite this

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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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N2 - 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.

AB - 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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DO - 10.1007/s00220-017-3015-6

M3 - مقالة

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -

ℓ ² Bounded Variation and Absolutely Continuous Spectrum of Jacobi Matrices

Abstract

All Science Journal Classification (ASJC) codes

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