Department of Mathematics 253--37, California Institute of Technology, Pasadena, California 91125 ; Department of Mathematics 253--37, California Institute of Technology, Pasadena, California 91125
Abstract:
We prove a criterion for absence of decaying solutions for one-dimensional Schrödinger operators. As necessary input, we require infinitely many centers of local reflection symmetry and upper and lower bounds for the traces of the associated transfer matrices.