David Damanik & Gunter Stolz
We present a criterion for absence of eigenvalues for one-dimensional Schrodinger operators. This criterion can be regarded as an L^1-version of Gordon's theorem and it has a broader range of application. Absence of eigenvalues is then established for quasiperiodic potentials generated by Liouville frequencies and various types of functions such as step functions, Holder continuous functions and functions with power-type singularities. The proof is based on Gronwall-type a priori estimates for solutions of Schrodinger equations.
Submitted May 12, 2000. Published July 18, 2000.
Math Subject Classifications: 34L05, 34L40, 81Q10.
Key Words: Schrodinger operators, eigenvalue problem, quasiperiodic potentials.
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Department of Mathematics, University of Alabama at Birmingham
Birmingham, AL 35294, USA