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Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian

  • Author(s): Damanik, D
  • Gorodetski, A
  • Solomyak, B
  • et al.
Abstract

© 2015. We prove for the square Fibonacci Hamiltonian that the density of states measure is absolutely continuous for almost all pairs of small coupling constants. This is obtained from a new result we establish about the absolute continuity of convolutions of measures arising in hyperbolic dynamics with exact-dimensional measures.

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