00-472 D. DAMANIK, J.-M. GHEZ, L. RAYMOND

A PALINDROMIC HALF-LINE CRITERION FOR ABSENCE OF EIGENVALUES AND APPLICATIONS TO SUBSTITUTION HAMILTONIANS (185K, PostScript) Nov 29, 00

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

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