A palindromic half-line criterion for absence of eigenvalues and applications to substitution Hamiltonians

We prove a criterion for absence of decaying solutions on the half-line for one-dimensional discrete Schrodinger operators. As necessary inputs, we re quire infinitely many palindromic prefixes and upper and lower bounds for t he traces of associated transfer matrices. We apply this criterion to Schro dinger operators with potentials generated by substitutions.