Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian
- Author(s): Damanik, D
- Gorodetski, A
- Solomyak, B
- et al.
Published Web Locationhttps://doi.org/10.1215/00127094-3119739
© 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.