ℓ2 Bounded Variation and Absolutely Continuous Spectrum of Jacobi Matrices

ℓ2 Bounded Variation and Absolutely Continuous Spectrum of Jacobi Matrices

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 ℓ 2 bounded variation condition with step q . We prove existence of a.c. spectrum on a smaller set than...

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Veröffentlicht in:Communications in mathematical physics 2018, Vol.359 (1), p.101-119
Hauptverfasser: Last, Yoram, Lukic, Milivoje
Format: Artikel
Sprache:eng
Schlagworte:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Zusammenfassung: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 ℓ 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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-017-3015-6