Abstract : We study spectral properties of a family of (Hp, x)x in X, indexed by a non-negative integer p, of one-dimensional discrete operators associated to an ergodic dynamical system (T, X, B, µ) and defined for u in l2(Z) and n in Z by (Hp,x u)(n) = u(n-p)+ u(n+p) + Vx(n)u(n), where Vx(n) = f(T^n x) and f is a real-valued measurable bounded map on X. In some particular cases, we prove that the nature of the spectrum does not change with p. Applications include some classes of random and quasi-periodic substitutional potentials.
https://hal-amu.archives-ouvertes.fr/hal-02012523 Contributor : Claire Guille-Biel WinderConnect in order to contact the contributor Submitted on : Friday, February 8, 2019 - 5:29:53 PM Last modification on : Sunday, June 26, 2022 - 10:18:49 AM Long-term archiving on: : Thursday, May 9, 2019 - 4:21:38 PM