ℓ2 Bounded Variation and Absolutely Continuous Spectrum of Jacobi Matrices
Sign Up to like & getrecommendations! Published in 2017 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-017-3015-6
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… read more here.
Keywords: bounded variation; spectrum jacobi; spectrum; absolutely continuous ... See more keywords
Spectral approximation for ergodic CMV operators with an application to quantum walks
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2018.06.056
Abstract: We establish concrete criteria for fully supported absolutely continuous spectrum for ergodic CMV matrices and purely absolutely continuous spectrum for limit-periodic CMV matrices. We proceed by proving several variational estimates on the measure of the… read more here.
Keywords: cmv; spectral approximation; cmv matrices; ergodic cmv ... See more keywords
Upper and lower absolutely continuous functions with applications to discontinuous differential equations
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DOI: 10.14232/ejqtde.2017.1.83
Abstract: We use upper and lower absolutely continuous functions as subsolutions and supersolutions to discontinuous ordinary differential equations. We present sufficient conditions for the existence of extremal solutions to initial value problems. Due to a new… read more here.
Keywords: upper lower; continuous functions; equations upper; differential equations ... See more keywords
A counter example on a Borsuk conjecture
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DOI: 10.4995/agt.2023.18176
Abstract: The study of shape restrictions of subsets of Rd has several applications in many areas, being convexity, r-convexity, and positive reach, some of the most famous, and typically imposed in set estimation. The following problem… read more here.
Keywords: absolutely continuous; counter example; borsuk; example borsuk ... See more keywords