On the Spectra of Sieved Schrödinger Operators

We give a family of examples of discrete Schrödinger operators whose spectral dimension is not invariant under sieving. The examples are produced from the Fibonacci Hamiltonian, which is one of the main models of a one-dimensional quasicrystal. We also give a family of examples in which the local Hausdorff dimension tends to zero in some parts of the spectrum as the sieving parameter is sent to infinity.