TY - JOUR
T1 - ℓ 2 Bounded Variation and Absolutely Continuous Spectrum of Jacobi Matrices
AU - Last, Yoram
AU - Lukic, Milivoje
N1 - Publisher Copyright:
© 2017, Springer-Verlag GmbH Germany.
PY - 2018/4/1
Y1 - 2018/4/1
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.
UR - http://www.scopus.com/inward/record.url?scp=85032831324&partnerID=8YFLogxK
U2 - 10.1007/s00220-017-3015-6
DO - 10.1007/s00220-017-3015-6
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AN - SCOPUS:85032831324
SN - 0010-3616
VL - 359
SP - 101
EP - 119
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 1
ER -