98-132 C. Remling

Bounds on embedded singular spectrum for one-dimensional Schroedinger operators (30K, LaTeX 2e) Mar 4, 98

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Abstract. Consider the 1D Schroedinger equation -y''+Vy=Ey with potential V bounded by |V(x)| < C(1+x)^{-c}. We prove that the solutions y satisfy the WKB asymptotic formulae off a set of energies E of Hausdorff dimension \le 2(1-c). This gives restrictions on the structure of possible embedded singular spectrum.

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