A Palindromic Half-Line Criterion for Absence of Eigenvalues and Applications to Substitution Hamiltonians

Abstract

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