Schrödinger Operators Generated by Locally Constant Functions on the Fibonacci Subshift

We investigate the spectral properties of discrete one-dimensional Schrodinger operators whose potentials are generated by sampling along the elements of the Fibonacci subshift with a locally constant function. The fundamental trace map formalism for this model is presented and related to its spectral features via an extension of a multitude of works on the classical model, where the sampling function only depends on a single entry of the sequence.