The Spectrum of the Quaquaversal Operator is Real
The Hecke operator associated with the Quaquaversal tiling, a highly anisotropic tiling introduced by Conway and Radin, is shown to have a real spectrum. Answering a question of Draco, Sadun, and Van Wieren. We also explicitly compute about three quarters of this operator's eigenvalues.
math.SP↗