, Volume 2, Issue 5, pp 927-939

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

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Abstract.

We prove a criterion for absence of decaying solutions on the half-line for one-dimensional discrete Schrödinger 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 Schrödinger operators with potentials generated by substitutions.

Submitted 12/10/00, accepted 07/06/01